Sz\303\241m\303\255t\303\263g\303\251pes sz\303\241melm\303\251let J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak

restart; with(numtheory);

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

[i$i=1..20]; evalf(map(i->log[2](mersenne([i])+1),%));

NzYiIiIiIiMiIiQiIiUiIiYiIiciIigiIikiIioiIzUiIzYiIzciIzgiIzkiIzoiIzsiIzwiIz0iIz4iIz8=

NzYkIiIjIiIhJCIiJEYlJCIiJkYlJCIiKEYlJCIjOEYlJCIjPEYlJCIjPkYlJCIjSkYlJCIjaEYlJCIjKilGJSQiJDIiRiUkIiRGIkYlJCIkQCZGJSQiJDInRiUkIiV6N0YlJCIlLkFGJSQiJSJHI0YlJCIlPEtGJSQiJWBVRiUkIiVCV0Yl

primeprod:=proc(n) local p,i; p:=1; for i from 2 to n do if isprime(i) then p:=p*i fi od; p,log[2.](p); end;

Zio2I0kibkc2IjYkSSJwR0YlSSJpR0YlRiVGJUMlPkYnIiIiPyhGKCIiI0YrRiRJJXRydWVHJSpwcm90ZWN0ZWRHQCQtSShpc3ByaW1lRzYkRi9JKF9zeXNsaWJHRiU2I0YoPkYnKiZGJ0YrRihGKzYkRictJkkkbG9nR0YzNiMkRi0iIiE2I0YnRiVGJUYl

primeprod(16);

NiQiJkkrJCQiKyZvNnVbIiEiKQ==

primeprod(32);

NiQiLUksXGcwPyQiK1pZX2FQISIp

primeprod(64);

NiQiOXFLKTQocFNmOFEpRzwiJCIrSDFXanchIik=

primeprod(128);

NiQiUkl4QyYpZWtPXi9FISo+VFc0Kj1PSUxScFo5UyQiKzF3ZDk7ISIo

primeprod(256);

NiQiYHFJLVVNS3UrX19fSnEhKXlPXSIpKjNvZVpDOSIzIzQ7Zic9ISkzSjhuNUdfaklCKFtrM3oiNExtVSckIitFKG8oW0whIig=

primeprod(512);

NiQiX3hJUzlAYD9hQDRVXSlcJEhzdDUlKj0yTkQocDlcMCwkcG0oPWZ4biE0NyUqcCJmZShwOCc9YS1NSD1kKW81MiMpekp6ISlISSYpKXlVeDJHRyl6bUlDPU87XzRJUFQlKj0qZjBHclxSRklEdVNZYikpbz4oRyIzaz4kJCIrJ3pLZy0oISIo

primeprod(1024);

NiQiZ2VsSWxqKEdXXDBnQTZPLTUnZmVdKG9GbWc5dzBwJW9lYHhlSSI+LlgkKVs4TyhSSyg+Zj5UKCkzK2ZfaUxNW29NQUVkelhuIVJLb00wNG8wQyUqZVh3QzYyKTQ/Si49bWp3VU1jbDNEQl1yRXJOJikpb2h4citqWE9xQExbU04+I3oxODc2QjAjR0Q7TFFdKWVnc3hKIilRdihmRUkzKCk9KDMpZikzJXAsVlpHNCR6JCpRSidbQGQpMztqRyhlIj5JV2lHKD1kOT1TeStcU3R1KyopbyZHbG9zWHVHUz9mJnlpXyE9KHA9V2FEJDMjJCIrT0BfPjkhIic=

primeprod(2048);

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

pd16:=1/ln(2.)/16; # approximate density of primes <=16 bit

JCIrMVMlbywqISM2

p16:=2.^16/ln(2.)/16; # approximate number of primes <=16 bit

JCIrKSkpeSM0ZiEiJw==

pd32:=1/ln(2.)/32; # approximate density of primes <=32 bit

JCIrLj9VM1ghIzY=

p32:=2.^32/ln(2.)/32; # approximate number of primes <=32 bit

JCIrMUROTz4hIiI=

pd35:=1/ln(2.)/35; # approximate density of primes <=35 bit

JCIrSmUpPjclISM2

p35:=2.^35/ln(2.)/35; # approximate number of primes <=35 bit

JCIrWk5JOzkiIiE=

pd40:=1/ln(2.)/40; # approximate density of primes <=40 bit

JCIrLXd0MU8hIzY=

p40:=2.^40/ln(2.)/40; # approximate number of primes <=40 bit

JCIrTCpcYydSIiIi

pd50:=1/ln(2.)/50; # approximate density of primes <=50 bit

JCIrIzMhUiYpRyEjNg==

p50:=2.^50/ln(2.)/50; # approximate number of primes <=50 bit

JCIrRC9tW0siIiU=

pd64:=1/ln(2.)/64; # approximate density of primes <=64 bit

JCIrLTVAYUEhIzY=

p64:=2.^64/ln(2.)/64; # approximate number of primes <=64 bit

JCIrVmBHZVQiIik=

# # This procedure approximate Cs calculating the product # for primes below x. # Cs:=proc(s::posint,x::posint) local P,p; P:=1.; p:=nextprime(s); while p<x do P:=P*(1-s/p)/(1-1/p)^s; p:=nextprime(p) od; P end;

Zio2JCdJInNHNiJJJ3Bvc2ludEclKnByb3RlY3RlZEcnSSJ4R0YmRic2JEkiUEdGJkkicEdGJkYmRiZDJj5GLCQiIiIiIiE+Ri0tSSpuZXh0cHJpbWVHNiRGKEkoX3N5c2xpYkdGJjYjRiU/KEYmRjFGMUYmMkYtRipDJD5GLCooRixGMSwmRjFGMSomRiVGMUYtISIiRkBGMSksJkYxRjEqJEYtRkBGQEYlRkA+Ri0tRjU2I0YtRixGJkYmRiY=

Cs(2,10); Cs(2,100); Cs(2,1000); Cs(2,10000); Cs(2,100000); Cs2:=Cs(2,1000000);

JCIrKVxQZiRvISM1

JCIrWTN4OG0hIzU=

JCIrWnVYLW0hIzU=

JCIrdUhvLG0hIzU=

JCIrR01pLG0hIzU=

JCIrbSQ9O2cnISM1

Cs(3,10); Cs(3,100); Cs(3,1000); Cs(3,10000); Cs(3,100000); Cs3:=Cs(3,1000000);

JCIrcS43KjMoISM1

JCIrXSdScFEnISM1

JCIrP3MzYWohIzU=

JCIrKzEmPU4nISM1

JCIrSSl5O04nISM1

JCIrL1ttXmohIzU=

Cs(4,10); Cs(4,100); Cs(4,1000); Cs(4,10000); Cs(4,100000); Cs4:=Cs(4,1000000);

JCIrLkYnbyhRISM1

JCIrLzRMNEohIzU=

JCIrZW5IeEkhIzU=

JCIrUSpIXjIkISM1

JCIrSE8nXDIkISM1

JCIrPywmXDIkISM1

Cs(5,10); Cs(5,100); Cs(5,1000); Cs(5,10000); Cs(5,100000); Cs5:=Cs(5,1000000);

JCIrQTpUdmghIzU=

JCIrJSpScnZUISM1

JCIrQCNvUjUlISM1

JCIrczc6KjQlISM1

JCIrPjx5KTQlISM1

JCIrXTp2KTQlISM1

Cs(6,10); Cs(6,100); Cs(6,1000); Cs(6,10000); Cs(6,100000); Cs6:=Cs(6,1000000);

JCIrKlFCQmckISM1

JCIrcidmIj4+ISM1

JCIrPyo0KHA9ISM1

JCIrP3lUbT0hIzU=

JCIrZmE7bT0hIzU=

JCIrbFs5bT0hIzU=

Cs(7,10); Cs(7,100); Cs(7,1000); Cs(7,10000); Cs(7,100000); Cs7:=Cs(7,1000000);

JCIiIiIiIQ==

JCIrJ1tMRiVRISM1

JCIrJFJvVXEkISM1

JCIrT3A4JnAkISM1

JCIrJEdQV3AkISM1

JCIrJD4hUSVwJCEjNQ==

Cs(8,10); Cs(8,100); Cs(8,1000); Cs(8,10000); Cs(8,100000); Cs8:=Cs(8,1000000);

JCIiIiIiIQ==

JCIrTz4oKlxDISM1

JCIrMygpXEtCISM1

JCIrPEMkW0sjISM1

JCIrUWJDQ0IhIzU=

JCIrMng+Q0IhIzU=

evalf(9*exp(-2*gamma)*Cs(3,10)); evalf(9*exp(-2*gamma)*Cs(3,100)); evalf(9*exp(-2*gamma)*Cs(3,1000)); evalf(9*exp(-2*gamma)*Cs(3,10000)); evalf(9*exp(-2*gamma)*Cs(3,100000)); evalf(9*exp(-2*gamma)*Cs(3,1000000));

JCIrXGhGNj8hIio=

JCIrKEhlPyI9ISIq

JCIrTHd0LT0hIio=

JCIrdkk1LT0hIio=

JCIrVFYwLT0hIio=

JCIraS4wLT0hIio=

# Twin prime, old f1:=h->(3.+30*h)*2.^38880.-1; f2:=f1+2; f2(1); g:=h->1/ln(f1(h))/ln(f2(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIiJCIiISIiIiwkKiYiI0lGL0YkRi9GL0YvRi8pJCIiI0YuJCImISkpUUYuRi9GL0YvISIiRiVGJUYl

LCZJI2YxRzYiIiIiIiIjRiU=

JCIrNixucU8iJidwNg==

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyRiVGJUYl

H:=2.^27; H/6*(g(0)+4*g(H/2)+g(H));

JCIqR3hATSIiIiE=

JCIrZ0VgWD0hIzU=

Cf1f2:=C2*(1-1/3)^2/(1-2/3)*(1-1/5)^2/(1-2/5)/(1-1/2)^2/(1-1/3)^2/(1-1/5)^2;

LCQqJiIjPyIiIkkjQzJHNiJGJUYl

%%*20*Cs2;

JCIraC9xT0MhIio=

f1:=h->(5775.+30030*h)*2.^171960.-1; f2:=f1+2; f2(1); g:=h->1/ln(f1(h))/ln(f2(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIldmQiIiEiIiIsJComIiZJKyRGL0YkRi9GL0YvRi8pJCIiI0YuJCInZz48Ri5GL0YvRi8hIiJGJUYlRiU=

LCZJI2YxRzYiIiIiIiIjRiU=

JCIrYSsjKilwJSImZzwm

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyRiVGJUYl

H:=2.^35; H/6*(g(0)+4*g(H/2)+g(H));

JCIrUFEoZlYkIiIi

JCIrWy1HPEMhIio=

C2*(1-1/3)^2/(1-2/3)*(1-1/5)^2/(1-2/5)*(1-1/7)^2/(1-2/7)*(1-1/11)^2/(1-2/11)*(1-1/13)^2/(1-2/13);

LCQqJiMiJiVROyImNjUiIiIiSSNDMkc2IkYnRic=

Cf1f2:=%/(1-1/2)^2/(1-1/3)^2/(1-1/5)^2/(1-1/7)^2/(1-1/11)^2/(1-1/13)^2;

LCQqJiMiJGskIiIqIiIiSSNDMkc2IkYnRic=

%*%%%; subs(C2=Cs2,%);

LCQqJiQiK3FjYncoKiEiKSIiIkkjQzJHNiJGJ0Yn

JCIrWiozVFgnISIp

# Cunningham chain I, length 3 f1:=h->(3.+78*h)*2.^(273*128)-1; f2:=2*f1+1; f3:=2*f2+1; f3(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIiJCIiISIiIiwkKiYiI3lGL0YkRi9GL0YvRi8pJCIiI0YuIiZXXCRGL0YvRi8hIiJGJUYlRiU=

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiVGJQ==

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkRiU=

JCIrIXklR1ZdIiY3MCI=

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKigtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjJGJUYlRiU=

H:=2.^40; H/6*(g(0)+4*g(H/2)+g(H));

JCIrRzteKjQiIiIk

JCIrJDNQO3IoISM2

Cf1f2f3:=C3/(1-1/2)^3/(1-1/3)^3*(1-1/13)^3/(1-3/13);

LCQqJiMiJkdMIyIkWCkiIiJJI0MzRzYiRidGJw==

%*%%; subs(C3=Cs3,%); HCCI3:=H/%;

LCQqJiQiKzIlZipHQCEiKiIiIkkjQzNHNiJGJ0Yn

JCIrYE9DXzghIio=

JCIrNXIsSiIpIiIj

# Cunningham chain I, length 4 f1:=h->(375.+390*h)*2.^(77*128)-1; f2:=2*f1+1; f3:=2*f2+1; f4:=2*f3+1; f4(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIkdiQiIiEiIiIsJComIiQhUkYvRiRGL0YvRi9GLykkIiIjRi4iJWMpKkYvRi9GLyEiIkYlRiVGJQ==

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiVGJQ==

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkRiU=

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoRiU=

JCIrQXYwdmEiJWhI

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiotSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMkYlRiVGJQ==

H:=2.^47; H/6*(g(0)+4*g(H/2)+g(H));

JCIrJSlbUDI5IiIm

JCIrZG1STmohIzY=

Cf1f2f3f4:=C4*(1-1/2)/(1-1/2)^4*(1-2/3)/(1-1/3)^4*(1-3/7)/(1-4/7)*(1-1/5)^4/(1-4/5)*(1-1/13)^4/(1-4/13);

LCQqJiMiKUtvaDUiJ0RZRiIiIkkjQzRHNiJGJ0Yn

%*%%; subs(C4=Cs4,%); HCCI4:=H/%;

LCQqJiQiKzldQVxDISIqIiIiSSNDNEc2IkYnRic=

JCIrXlpDSnYhIzU=

JCIrVFtybz0iIiY=

# Cunningham chain I, length 5 f1:=h->(255.+390*h)*2.^(32*128)-1; f2:=2*f1+1; f3:=2*f2+1; f4:=2*f3+1; f5:=2*f4+1; f5(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIkYiMiIiEiIiIsJComIiQhUkYvRiRGL0YvRi9GLykkIiIjRi4iJSc0JUYvRi9GLyEiIkYlRiVGJQ==

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiVGJQ==

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkRiU=

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoRiU=

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6RiU=

JCIrRCQ0eTIiIiVHNw==

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiwtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMi1GKzYjLUkjZjVHRiVGI0YyRiVGJUYl

H:=2.^54; H/6*(g(0)+4*g(H/2)+g(H));

JCIrXilSOSE9IiIo

JCIrcUFaUyIqISM2

Cf1f2f3f4f5:=C5*(1-1/2)/(1-1/2)^5*(1-2/3)/(1-1/3)^5*(1-4/5)/(1-1/5)^5*(1-2/7)/(1-4/7)*(1-1/13)^5/(1-5/13)*(1-7/17)/(1-5/17);

LCQqJiMiKXY9PE0iJ19SIioiIiJJI0M1RzYiRidGJw==

%*%%; subs(C5=Cs5,%); HCCI5:=H/%;

LCQqJiQiK1lOYTxNISIqIiIiSSNDNUc2IkYnRic=

JCIrIj5tMlMiISIq

JCIrRypRZ0ciIiIo

# Cunningham chain I, length 6 f1:=h->(375.+390*h)*2.^(29*64)-1; f2:=2*f1+1; f3:=2*f2+1; f4:=2*f3+1; f5:=2*f4+1; f6:=2*f4+1; f6(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h))/ln(f6(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIkdiQiIiEiIiIsJComIiQhUkYvRiRGL0YvRi9GLykkIiIjRi4iJWM9Ri9GL0YvISIiRiVGJUYl

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiVGJQ==

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkRiU=

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoRiU=

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6RiU=

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6RiU=

JCIrQG9qLGoiJGAm

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKi4tSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMi1GKzYjLUkjZjVHRiVGI0YyLUYrNiMtSSNmNkdGJUYjRjJGJUYlRiU=

H:=2.^60; H/6*(g(0)+4*g(H/2)+g(H));

JCIrMDojSDoiIiIq

JCIrITQmcDBAISM1

Cf1f2f3f4f5f6:=C6*(1-1/2)/(1-1/2)^6*(1-2/3)/(1-1/3)^6*(1-4/5)/(1-1/5)^6*(1-1/7)/(1-4/7)*(1-1/13)^6/(1-6/13)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31);

LCQqJiMiKl0tJ0c4IigoPio+IyIiIkkjQzZHNiJGJ0Yn

%*%%; subs(C6=Cs6,%); HCCI6:=H/%;

LCQqJiQiK0FeNnM3ISIpIiIiSSNDNkc2IkYnRic=

JCIrLjYmUlAjISIq

JCIrKT1ebCZbIiIp

# Cunningham chain I, length 6 f1:=h->(375.+2*3*5*7*11*13*17*19*23*29*31*37*41*47*53*59*61*67*h)*2.^(29*64)-1; f2:=2*f1+1; f3:=2*f2+1; f4:=2*f3+1; f5:=2*f4+1; f6:=2*f4+1; f6(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h))/ln(f6(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIkdiQiIiEiIiIsJComIjlJWXdoM2h5Um1eRj1GL0YkRi9GL0YvRi8pJCIiI0YuIiVjPUYvRi9GLyEiIkYlRiVGJQ==

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiVGJQ==

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkRiU=

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoRiU=

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6RiU=

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6RiU=

JCIrRVpTMDoiJHUm

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKi4tSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMi1GKzYjLUkjZjVHRiVGI0YyLUYrNiMtSSNmNkdGJUYjRjJGJUYlRiU=

H:=2.^60; H/6*(g(0)+4*g(H/2)+g(H));

JCIrMDojSDoiIiIq

JCIrUzM3JXkiISM1

Cf1f2f3f4f5f6:=C6*(1-1/2)/(1-1/2)^6*(1-2/3)/(1-1/3)^6*(1-4/5)/(1-1/5)^6*(1-1/7)/(1-4/7)*(1-1/13)^6/(1-6/13)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31);

LCQqJiMiKl0tJ0c4IigoPio+IyIiIkkjQzZHNiJGJ0Yn

%*%%; subs(C6=Cs6,%); HCCI61:=H/%;

LCQqJiQiK01BJXkyIiEiKSIiIkkjQzZHNiJGJ0Yn

JCIrXSg0OSwjISIq

JCIrM3ghPnQmIiIp

# Cunnigham chain II, length 2 + twinprime f1:=h->(5775.+30030*h)*2.^(1983*128)-1; f2:=f1+2; f3:=2*f2-1; f3(1); g:=h->1/ln(f1(h))/ln(f3(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIldmQiIiEiIiIsJComIiZJKyRGL0YkRi9GL0YvRi8pJCIiI0YuIidDUURGL0YvRi8hIiJGJUYlRiU=

LCZJI2YxRzYiIiIiIiIjRiU=

LCYqJiIiIyIiIkkjZjFHNiJGJUYlIiIkRiU=

JCIrIz0tKTNKIiYvayg=

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjNHRiVGI0YyRiVGJUYl

H:=2.^35; H/6*(g(0)+4*g(H/2)+g(H));

JCIrUFEoZlYkIiIi

JCIrdG9rNDYhIio=

C2*(1-1/3)^2/(1-2/3)*(1-1/5)^2/(1-2/5)*(1-1/7)^2/(1-2/7)*(1-1/11)^2/(1-2/11)*(1-1/13)^2/(1-2/13);

LCQqJiMiJiVROyImNjUiIiIiSSNDMkc2IkYnRic=

Cf1f3:=%/(1-1/2)^2/(1-1/3)^2/(1-1/5)^2/(1-1/7)^2/(1-1/11)^2/(1-1/13)^2;

LCQqJiMiJGskIiIqIiIiSSNDMkc2IkYnRic=

%*%%%; subs(C2=Cs2,%);

LCQqJiQiK0peIXpbJSEiKSIiIkkjQzJHNiJGJ0Yn

JCIrJXBWRidIISIp

# Cunningham chain II, length 3 f1:=h->(3.+6*h)*2.^(247*128)+1; f2:=2*f1-1; f3:=2*f2-1; f3(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIiJCIiISIiIiwkKiYiIidGL0YkRi9GL0YvRi8pJCIiI0YuIiY7OyRGL0YvRi9GL0YlRiVGJQ==

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiUhIiI=

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkISIi

JCIrK3orSSQpIiU0Jio=

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKigtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjJGJUYlRiU=

H:=2.^43; H/6*(g(0)+4*g(H/2)+g(H));

JCIrQUk0J3opIiIk

JCIrbi9JRiQpISM1

Cf1f2f3:=C3*(1-1/2)/(1-1/2)^3*(1-2/3)/(1-1/3)^3;

LCQqJiMiIioiIiMiIiJJI0MzRzYiRidGJw==

%*%%; subs(C3=Cs3,%); HCCII3:=H/%;

LCQqJiQiKzVfR1pQISIqIiIiSSNDM0c2IkYnRic=

JCIrZSpcLFEjISIq

JCIrYFhnJnAkIiIk

# Cunningham chain II, length 4 f1:=h->(15.+30*h)*2.^(61*128)+1; f2:=2*f1-1; f3:=2*f2-1; f4:=2*f3-1; f4(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIjOiIiISIiIiwkKiYiI0lGL0YkRi9GL0YvRi8pJCIiI0YuIiUzeUYvRi9GL0YvRiVGJUYl

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiUhIiI=

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkISIi

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoISIi

JCIrdyI+ZCcqKiIlVkI=

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiotSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMkYlRiVGJQ==

H:=2.^49; H/6*(g(0)+4*g(H/2)+g(H));

JCIrTSYqXEhjIiIm

JCIrMkNCM2shIzU=

Cf1f2f3f4:=C4*(1-1/2)/(1-1/2)^4*(1-2/3)/(1-1/3)^4*(1-4/5)/(1-1/5)^4*(1-3/7)/(1-4/7);

LCQqJiMiJUQ2IiRHIiIiIkkjQzRHNiJGJ0Yn

%*%%; subs(C4=Cs4,%); HCCII4:=H/%;

LCQqJiQiKzliQktjISIqIiIiSSNDNEc2IkYnRic=

JCIrRlYpPXQiISIq

JCIrLWJdXUsiIiY=

# Cunningham chain II, length 5 f1:=h->(15.+30*h)*2.^(30*128)+1; f2:=2*f1-1; f3:=2*f2-1; f4:=2*f3-1; f5:=2*f4-1; f5(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIjOiIiISIiIiwkKiYiI0lGL0YkRi9GL0YvRi8pJCIiI0YuIiVTUUYvRi9GL0YvRiVGJUYl

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiUhIiI=

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkISIi

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoISIi

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6ISIi

JCIraEswJVwnIiVcNg==

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiwtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMi1GKzYjLUkjZjVHRiVGI0YyRiVGJUYl

H:=2.^54; H/6*(g(0)+4*g(H/2)+g(H));

JCIrXilSOSE9IiIo

JCIrI3lyRkUiISM1

Cf1f2f3f4f5:=C5*(1-1/2)/(1-1/2)^5*(1-2/3)/(1-1/3)^5*(1-4/5)/(1-1/5)^5*(1-2/7)/(1-4/7);

LCQqJiMiJnZWKSIlWz8iIiJJI0M1RzYiRidGJw==

%*%%; subs(C5=Cs5,%); HCCII5:=H/%;

LCQqJiQiK0glZkM/JiEiKiIiIkkjQzVHNiJGJ0Yn

JCIrbCllQjgjISIq

JCIrWSMzIlslKSIiJw==

# Cunningham chain II, length 6 f1:=h->(15.+30*h)*2.^(29*64)+1; f2:=2*f1-1; f3:=2*f2-1; f4:=2*f3-1; f5:=2*f4-1; f6:=2*f4-1; f6(1); g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h))/ln(f6(h));

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiwmJCIjOiIiISIiIiwkKiYiI0lGL0YkRi9GL0YvRi8pJCIiI0YuIiVjPUYvRi9GL0YvRiVGJUYl

LCYqJiIiIyIiIkkjZjFHNiJGJUYlRiUhIiI=

LCYqJiIiJSIiIkkjZjFHNiJGJUYlIiIkISIi

LCYqJiIiKSIiIkkjZjFHNiJGJUYlIiIoISIi

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6ISIi

LCYqJiIjOyIiIkkjZjFHNiJGJUYlIiM6ISIi

JCIrKj1Yb3EkIiRfJg==

Zio2I0kiaEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKi4tSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjZjFHRiVGIyEiIi1GKzYjLUkjZjJHRiVGI0YyLUYrNiMtSSNmM0dGJUYjRjItRis2Iy1JI2Y0R0YlRiNGMi1GKzYjLUkjZjVHRiVGI0YyLUYrNiMtSSNmNkdGJUYjRjJGJUYlRiU=

H:=2.^58; H/6*(g(0)+4*g(H/2)+g(H));

JCIraVBJIylHIiIp

JCIrX3h0YmAhIzY=

Cf1f2f3f4f5f6:=C6*(1-1/2)/(1-1/2)^6*(1-2/3)/(1-1/3)^6*(1-4/5)/(1-1/5)^6*(1-1/7)/(1-4/7)*(1-5/31)/(1-6/31);

LCQqJiMiJ3ZbUiIlWz8iIiJJI0M2RzYiRidGJw==

%*%%; subs(C6=Cs6,%); HCCII6:=H/%;

LCQqJiQiKzUsa0s1ISIpIiIiSSNDNkc2IkYnRic=

JCIrUmcwRj4hIio=

JCIrUEpxJlwiIiIp

sieve:=proc(N::posint) local n,B,i,j; n:=floor((N-1)/2); B:=Array(0..n-1); for j from 0 to n-1 do B[j]:=1 od; j:=0; while j<n do while B[j]=0 do j:=j+1 od; i:=2*j^2+6*j+3; if i>=n then break fi; while i<n do B[i]:=0; i:=i+2*j+3 od; j:=j+1; od; B; end;

Zio2IydJIk5HNiJJJ3Bvc2ludEclKnByb3RlY3RlZEc2JkkibkdGJkkiQkdGJkkiaUdGJkkiakdGJkYmRiZDKD5GKi1JJmZsb29yR0YmNiMsJiomIyIiIiIiI0Y2RiVGNkY2RjUhIiI+RistSSZBcnJheUdGKDYjOyIiISwmRipGNkY2Rjg/KEYtRj5GNkY/SSV0cnVlR0YoPiZGKzYjRi1GNj5GLUY+PyhGJkY2RjZGJjJGLUYqQyc/KEYmRjZGNkYmL0ZDRj4+Ri0sJkYtRjZGNkY2PkYsLCgqJkY3RjYpRi1GN0Y2RjYqJiIiJ0Y2Ri1GNkY2IiIkRjZAJDFGKkYsWz8oRiZGNkY2RiYyRixGKkMkPiZGKzYjRixGPj5GLCwoRixGNiomRjdGNkYtRjZGNkZTRjZGS0YrRiZGJkYm

debug(sieve); sieve(21);

SSZzaWV2ZUc2Ig==

{--> enter sieve, args = 21

IiM1

LUkmQXJyYXlHJSpwcm90ZWN0ZWRHNiMvSSQlaWRHNiIiKmcoZjg6

IiIi

IiIi

IiIi

IiIi

IiIi

IiIi

IiIi

IiIi

IiIi

IiIi

IiIh

IiIk

IiIh

IiIn

IiIh

IiIq

IiIh

IiM3

IiIi

IiM2

LUkmQXJyYXlHJSpwcm90ZWN0ZWRHNiMvSSQlaWRHNiIiKmcoZjg6

<-- exit sieve (now at top level) = Array(0..9, {(1) = 1, (2) = 1, (3) = 1, (4) = 0, (5) = 1, (6) = 1, (7) = 0, (8) = 1, (9) = 1})}

LUkmQXJyYXlHJSpwcm90ZWN0ZWRHNiMvSSQlaWRHNiIiKmcoZjg6

undebug(sieve); sieve(10000);

SSZzaWV2ZUc2Ig==

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

# # This is a simple pretest for a number # using gcd. If there is a true divisor # below 1000 then the result is false else true. # pre:=proc(n::integer) local p; p:=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]; if n < 2 then false elif has(p,n) then true elif igcd(2305567963945518424753102147331756070,n) <> 1 then false elif n < 10201 then true elif igcd(\ 84969694892334181105323399091873499659260625866489327366115454263422038932\ 70769390909069477309509137509786917118668028861499333825097682386722983737\ 96296306675767413112673657893644078815718696989373063311306647862044862494\ 92573240226273954373636390387526081667586612559568346306972204475122988482\ 22228550062683786342519960225996301315945644470064720696621750477244528915\ 927867113,n) <> 1 then false else true fi end;

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

# # This simple routine do the the simple pretest for n+id, 0<=i<N. # The result is the list of i's not find to be composite. # preseq:=proc(n,d,N) local i,L; L:=[]; for i from 0 to N-1 do if pre(n+i*d) then L:=[op(L),i]; fi; od; L; end;

Zio2JUkibkc2IkkiZEdGJUkiTkdGJTYkSSJpR0YlSSJMR0YlRiVGJUMlPkYqNyI/KEYpIiIhIiIiLCZGJ0YwRjAhIiJJJXRydWVHJSpwcm90ZWN0ZWRHQCQtSSRwcmVHRiU2IywmRiRGMComRilGMEYmRjBGMD5GKjckLUkjb3BHRjQ2I0YqRilGKkYlRiVGJQ==

Digits:=10000; n:=ceil(Pi*10^4999): L:=preseq(n,2,30000):

IiYrKyI=

# # Calculation of the greatest common # divisor by the Euclidean algorithm. # eucgcd:=proc(x::integer,y::integer) local u,v,r; u:=abs(x); v:=abs(y); while v<>0 do r:=irem(u,v); u:=v; v:=r od; u end;

Zio2JCdJInhHNiJJKGludGVnZXJHJSpwcm90ZWN0ZWRHJ0kieUdGJkYnNiVJInVHRiZJInZHRiZJInJHRiZGJkYmQyY+RiwtSSRhYnNHRig2I0YlPkYtLUYyNiNGKj8oRiYiIiJGOEYmMEYtIiIhQyU+Ri4tSSVpcmVtR0YoNiRGLEYtPkYsRi0+Ri1GLkYsRiZGJkYm

# # Calculation of the modular inverse by the Euclidean # algorithm using division. # modinvdiv:=proc(a::integer,m::integer) local x1,x2,x3,d1,d2,d3,q,p; x1:=1; d1:=a; x2:=0; d2:=m; p:=0; do if d2=0 then if p=0 then return [x1,d1] elif x1=0 then return [x1,d1] else return [m-x1,d1] fi; fi; q:=iquo(d1,d2); d3:=d1-q*d2; x3:=x1+q*x2; p:=1-p; x1:=x2; x2:=x3; d1:=d2; d2:=d3; od; end;

Zio2JCdJImFHNiJJKGludGVnZXJHJSpwcm90ZWN0ZWRHJ0kibUdGJkYnNipJI3gxR0YmSSN4MkdGJkkjeDNHRiZJI2QxR0YmSSNkMkdGJkkjZDNHRiZJInFHRiZJInBHRiZGJkYmQyg+RiwiIiI+Ri9GJT5GLSIiIT5GMEYqPkYzRjk/KEYmRjZGNkYmSSV0cnVlR0YoQytAJC9GMEY5QCcvRjNGOU83JEYsRi8vRixGOUZDTzckLCZGKkY2RiwhIiJGLz5GMi1JJWlxdW9HRig2JEYvRjA+RjEsJkYvRjYqJkYyRjZGMEY2Rkk+Ri4sJkYsRjYqJkYyRjZGLUY2RjY+RjMsJkY2RjZGM0ZJPkYsRi0+Ri1GLj5GL0YwPkYwRjFGJkYmRiY=

modinvdiv(13874,15543);

NyQiJS4qKSIiIg==

# # Calculation of the greatest common # divisor by the binary algorithm. # bingcd:=proc(x::integer,y::integer) local u,v,k,t; u:=abs(x); v:=abs(y); if u=0 then RETURN(v) fi; if v=0 then RETURN(u) fi; k:=0; while type(u,even) and type(v,even) do k:=k+1; u:=u/2; v:=v/2 od; if type(u,odd) then t:=-v else t:=u fi; while t<>0 do while type(t,even) do t:=t/2 od; if t>0 then u:=t else v:=-t fi; t:=u-v; od; u*2^k end;

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

# # Calculation of the modular inverse with respect to an # odd modulus by the binary gcd algorithm. # oddmodinvbin:=proc(a::nonnegint,m::posint) local x1,x2,x3,d1,d2,d3,p; if not type(m,odd) then error "second argument have to be odd",m fi; if m=1 then return [0,1] fi; x1:=1; d1:=a mod m; x2:=m; d2:=m; if type(d1,even) then x3:=0; d3:=m; p:=1 else x3:=1; d3:=d1; p:=0 fi; while d3<>0 do while type(d3,even) do d3:=d3/2; if type(x3,even) then x3:=x3/2 else x3:=(x3+m)/2 fi; od; if p=0 then x1:=x3; d1:=d3 else x2:=m-x3; d2:=d3 fi; if x1>=x2 then x3:=x1-x2 else x3:=m+x1-x2 fi; if d1>=d2 then d3:=d1-d2; p:=0 else d3:=d2-d1; p:=1 fi; od; [x1,d1] end;

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

oddmodinvbin(13874,15543);

NyQiJS4qKSIiIg==

trymodinvs:=proc(n) local i,a,m,b,d; for i to n do a:=rand(); m:=rand(); if type(m,even) then m:=m+1; fi; a:=a mod m; d:=modinvdiv(a,m); b:=oddmodinvbin(a,m); if d[1]*a-d[2]mod m<>0 or b[1]*a-b[2] mod m<>0 then print(a,m,d,b) fi; od; end;

Zio2I0kibkc2IjYnSSJpR0YlSSJhR0YlSSJtR0YlSSJiR0YlSSJkR0YlRiVGJT8oRiciIiJGLUYkSSV0cnVlRyUqcHJvdGVjdGVkR0MpPkYoLUklcmFuZEc2JEYvSShfc3lzbGliR0YlRiU+RilGMkAkLUkldHlwZUdGLzYkRilJJWV2ZW5HRi8+RiksJkYpRi1GLUYtPkYoLUkkbW9kR0YlNiRGKEYpPkYrLUkqbW9kaW52ZGl2R0YlRkE+RiotSS1vZGRtb2RpbnZiaW5HRiVGQUAkNTAtRkA2JCwmKiYmRis2I0YtRi1GKEYtRi0mRis2IyIiIyEiIkYpIiIhMC1GQDYkLCYqJiZGKkZQRi1GKEYtRi0mRipGUkZURilGVS1JJnByaW50R0YvNiZGKEYpRitGKkYlRiVGJQ==

trymodinvs(10);

Digits:=10;

IiM1

# # This procedure calculate the sum of the reciprocal # of primes up to x and compare with ln(ln(x)). # sumprimerec:=proc(x) local s,p,i; s:=0.; p:=2; while p<x do s:=evalf(s+1/p); p:=nextprime(p) od; [s,evalf(s-ln(ln(x)))] end;

Zio2I0kieEc2IjYlSSJzR0YlSSJwR0YlSSJpR0YlRiVGJUMmPkYnJCIiIUYtPkYoIiIjPyhGJSIiIkYxRiUyRihGJEMkPkYnLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMsJkYnRjEqJEYoISIiRjE+RigtSSpuZXh0cHJpbWVHNiRGN0koX3N5c2xpYkdGJTYjRig3JEYnLUY2NiMsJkYnRjEtSSNsbkdGPzYjLUZHRiNGO0YlRiVGJQ==

sumprimerec(10); sumprimerec(100); sumprimerec(1000); sumprimerec(10000); sumprimerec(100000); sumprimerec(1000000);

NyQkIit3Lz53NiEiKiQiKzIuZUBNISM1

NyQkIisucyJHIT0hIiokIip4dmp2I0Yl

NyQkIitKLDMpPiMhIiokIiooUk5hRUYl

NyQkIitlKmZJWyMhIiokIipfSnRpI0Yl

NyQkIit5QEYwRiEiKiQiKkA9IT1FRiU=

NyQkIitTIkd0KUchIiokIipEaWBoI0Yl

# # This procedure calculate the factor qsAB. # qsAB:=proc(s::posint,A::posint,B::posint) local P,p; P:=1.; p:=nextprime(A-1); while p<B do P:=P*(1-s/p); p:=nextprime(p) od; P end;

Zio2JSdJInNHNiJJJ3Bvc2ludEclKnByb3RlY3RlZEcnSSJBR0YmRicnSSJCR0YmRic2JEkiUEdGJkkicEdGJkYmRiZDJj5GLiQiIiIiIiE+Ri8tSSpuZXh0cHJpbWVHNiRGKEkoX3N5c2xpYkdGJjYjLCZGKkYzRjMhIiI/KEYmRjNGM0YmMkYvRixDJD5GLiomRi5GMywmRjNGMyomRiVGM0YvRjxGPEYzPkYvLUY3NiNGL0YuRiZGJkYm

qsAB(1,1,100);

JCIrMEg8LjchIzU=

B:=10: [qsAB(1,1,B),evalf(qsAB(1,1,B)-exp(-gamma)/ln(B))]; B:=100: [qsAB(1,1,B),evalf(qsAB(1,1,B)-exp(-gamma)/ln(B))]; B:=1000: [qsAB(1,1,B),evalf(qsAB(1,1,B)-exp(-gamma)/ln(B))]; B:=10000: [qsAB(1,1,B),evalf(qsAB(1,1,B)-exp(-gamma)/ln(B))]; B:=100000: [qsAB(1,1,B),evalf(qsAB(1,1,B)-exp(-gamma)/ln(B))]; B:=1000000: [qsAB(1,1,B),evalf(qsAB(1,1,B)-exp(-gamma)/ln(B))];

NyQkIismRzlkRyMhIzUkISpxS25fIkYl

NyQkIiswSDwuNyEjNSQhKXQzLTtGJQ==

NyQkIitcal8nNCkhIzYkISluQFZKRiU=

NyQkIitRI3AlKTMnISM2JCEoXScqXChGJQ==

NyQkIitkPEh2WyEjNiQhKGBMWyJGJQ==

Warning, computation interrupted

qsAB(2,7,1000000);

Warning, computation interrupted

%*(ln(1000000.)/ln(44000.*2^25))^2;

JCIrZ1RqK2AhIzc=

# Cunningham chain I, length 3 f:=qsAB(3,16,64);

JCIrMztwJDMkISM1

f:=f*(1-3/5)*(1-3/7)*(1-3/11);

JCIrKnBPaDcmISM2

H:=HCCI3; H/8; H*f; 2*%;

JCIrNXIsSiIpIiIj

JCIrUnJQOzUiIiM=

JCIrQDAyb1QiIiI=

JCIrVTU5TyQpIiIi

P:=20; f0:=qsAB(3,16,P); f0:=f0*(1-3/5)*(1-3/7)*(1-3/11); HCCI30:=H*f0; %/8; 2*%%; log[2.](H*f0); primeprod(P); op(2,[%])+%%;

IiM/

JCIrP1gpXCRwISM1

JCIrJ2ZHRzoiISM1

JCIrbFxzJ1IqIiIh

JCIrQDFmdTYiIiE=

JCIrJCpcTXo9IiIi

JCIrKTNeSEokISIp

NiQiKCFwKnAqJCIrQDImNEsjISIp

JCIrND0hUmomISIp

P:=72; f1:=qsAB(3,16,P); f1:=f1*(1-3/5)*(1-3/7)*(1-3/11); HCCI31:=H*f1; %/8; 2*%%; log[2.](H*f1); primeprod(P); op(2,[%])+%%;

IiNz

JCIrQUs6QEchIzU=

JCIrXyM0KCpvJSEjNg==

JCIrPDFAOFEiIiI=

JCIrcktebVoiIiE=

JCIrTTdVRXciIiI=

JCIrPChHXV4kISIp

NiQiPCFSOnUnNCcqKXBFLCQzJXpiJCIrZ1UtJikpKSEiKQ==

JCIrKUgwK0MiISIo

P:=125; f:=qsAB(3,16,P); f:=f*(1-3/5)*(1-3/7)*(1-3/11); H*f; %/8; 2*%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiREIg==

JCIrZyIqKWYuIyEjNQ==

JCIraDldJVEkISM2

JCIrSFIlPnYjIiIi

JCIrNipIKlJNIiIh

JCIrQSlmKXpvIiIh

JCIrLUsoelkkISIp

NiQiUCEqcG91S1xpT2EiSDFfOSl5MndUU1kwNTskJCIrZjJwVzohIig=

JCIreiEpWyIqPSEiKA==

P:=165; f2:=qsAB(3,16,P); f2:=f2*(1-3/5)*(1-3/7)*(1-3/11); HCCI32:=H*f2; %/8; 2*%; log[2.](H*f2); primeprod(P); op(2,[%])+%%;

IiRsIg==

JCIrWSh5KT08ISM1

JCIrd29OZEchIzY=

JCIrbDxLQkIiIiI=

JCIrMUE6L0giIiE=

JCIrN1dJM2UiIiE=

JCIrIypwYVZNISIp

NiQiW281KW9nJik+ajExYywlUWxsSU1oTE4rakIhZjsmZigqPkE6bWQkIisqeSE0PUAhIig=

JCIrKVtYQ1kjISIo

f10:=qsAB(3,16,2^16); f10:=f10*(1-3/5)*(1-3/7)*(1-3/11); H*f10; 2*%;

JCIrejIpKVE8ISM2

JCIrNHFnISpHISM3

JCIrMHZOXUIiIiE=

JCIrNV1yK1oiIiE=

f13:=f10*(16/19)^3; H*f13; 2*%;

JCIrNiUpPUU8ISM3

JCIrXW5jLjkiIiE=

JCIrK044MkciIiE=

f15:=f13*(19/21)^3; H*f15; 2*%;

JCIrKm9yJXk3ISM3

JCIrPXZfUjUiIiE=

JCIrT10wej8iIiE=

f18:=f15*(21/24)^3; H*f18; 2*%;

JCIrNTp3ayYpISM4

JCIrUUEta3AhIiI=

JCIrW1chR1IiIiIh

f26:=f18*(24/32)^3; H*f26; 2*%;

JCIraShlS2gkISM4

JCIrIylvJXokSCEiIg==

JCIra1AqZShlISIi

f29:=f26*(32/35)^3; H*f26; 2*%;

JCIrWykpXGhGISM4

JCIrIylvJXokSCEiIg==

JCIra1AqZShlISIi

f34:=f29*(35/40)^3; H*f34; 2*%;

JCIrJ1spKSpcPSEjOA==

JCIrLilHVV0iISIi

JCIrMXdYM0khIiI=

f44:=f34*(40/50)^3; H*f44; 2*%;

JCIrWzUlPloqISM5

JCIrdDlsLHghIiM=

JCIrJkhJLmEiISIi

#64 bit multiplier H:=HCCI30; %/8; 2*%%; P:=20.;

JCIrbFxzJ1IqIiIh

JCIrQDFmdTYiIiE=

JCIrJCpcTXo9IiIi

JCIjPyIiIQ==

150*p50/3.2/10^9; # 64 bit reciprocal modulo primes <= 50 bit, sec

JCIrdSY0R18iISIk

# density and number after sieve with <=16 bit primes f10/f0; %*H;

JCIrelJTMkQhIzY=

JCIrZCZRaE4jISIi

# sieve events for <=16 bit primes 3*H*ln(16./ln(P));

JCIraj4pSHMlIiIi

# density and number after sieve with <=32 bit primes f26/f0; %*H;

JCIrdlxETUohIzc=

JCIrKD50XiVIISIj

# sieve events for <=32 bit primes 3*H*ln(32./ln(P));

JCIrJylmKHBuJyIiIg==

# sieve events for <=50 bit primes 3*H*ln(50./ln(P));

JCIrUHIxTnoiIiI=

%/0.8/10^9; # total sieve time in sec

JCIrQFIkKT0qKiEiKQ==

#128 bit multiplier H:=HCCI31; %/8; 2*%%; P:=72.;

JCIrPDFAOFEiIiI=

JCIrcktebVoiIiE=

JCIrTTdVRXciIiI=

JCIjcyIiIQ==

200*p50/3.2/10^9; # 128 bit reciprocal modulo primes <=50 bit, sec

JCIrbUZUST8hIiQ=

# density and number after sieve with <=16 bit primes f10/f1; %*H;

JCIrektzamghIzY=

JCIrMHZOXUIiIiE=

# sieve events for <=16 bit primes 3*H*ln(16./ln(P));

JCIrU0BPNDoiIiM=

# density and number after sieve with <=32 bit primes f26/f1; %*H;

JCIrLFRsL3ghIzc=

JCIrIylvJXokSCEiIg==

# sieve events for <=32 bit primes 3*H*ln(32./ln(P));

JCIrKCpwSC1CIiIj

# sieve events for <=50 bit primes 3*H*ln(50./ln(P));

JCIrOEkkRyJHIiIj

%/0.8/10^9; # total sieve time in sec

JCIrbTcvO04hIig=

#256 bit multiplier H:=HCCI32; %/8; 2*%%; P:=165.;

JCIrbDxLQkIiIiI=

JCIrMUE6L0giIiE=

JCIrSU5rWVkiIiI=

JCIkbCIiIiE=

300*p50/3.2/10^9; # 256 bit reciprocal modulo primes <=50 bit, sec

JCIrWyI+Yy8kISIk

# density and number after sieve with <=16 bit primes f10/f2; %*H;

JCIrdm1qNjUhIzU=

JCIrMHZOXUIiIiE=

# sieve events for <=16 bit primes 3*H*ln(16./ln(P));

JCIrVWsoNCd6IiIi

# density and number after sieve with <=32 bit primes f26/f2; %*H;

JCIrV2VhazchIzY=

JCIrIylvJXokSCEiIg==

# sieve events for <=32 bit primes 3*H*ln(32./ln(P));

JCIrQyk9I3o3IiIj

# sieve events for <=50 bit primes 3*H*ln(50./ln(P));

JCIrJ1F6LWYiIiIj

%/0.8/10^9; # total sieve time in sec

JCIrSyNceSk+ISIo

H*f44/f2*300/8^2/1.352243653; # SPU time in sec

JCIrN3Z1cEUhIiI=

%/24/3600/420; # time for all SPU in days

JCIrVyUzck4oISIq

# Cunningham chain I, length 4 f:=qsAB(4,16,64);

JCIrUDAyOT8hIzU=

f:=f*(1-3/7)*(1-4/11);

JCIraUcqUUsoISM2

H:=HCCI4; H/8; H*f; 2*%;

JCIrVFtybz0iIiY=

JCIrXk4qZUwjIiIl

JCIrSG5pbzgiIiU=

JCIrZU1EUEYiIiU=

P:=16; f0:=qsAB(4,16,P); f0:=f0*(1-3/7)*(1-4/11); HCCI40:=H*f0; %/8; 2*%%; log[2.](H*f0); primeprod(P); op(2,[%])+%%;

IiM7

JCIiIiIiIQ==

JCIrT09PT08hIzU=

JCIrJXBFYHonIiIl

JCIrbyRlVFwpIiIk

JCIrUmAxZjgiIiY=

JCIrOjMnXGYlISIp

NiQiJkkrJCQiKyZvNnVbIiEiKQ==

JCIrK0RQIzMnISIp

P:=65; f1:=qsAB(4,16,P); f1:=f1*(1-3/7)*(1-4/11); HCCI41:=H*f1; %/8; 2*%%; log[2.](H*f1); primeprod(P); op(2,[%])+%%;

IiNs

JCIrUDAyOT8hIzU=

JCIraUcqUUsoISM2

JCIrSG5pbzgiIiU=

JCIrNk15NTwiIiQ=

JCIrZU1EUEYiIiU=

JCIrRSV6UE8lISIp

NiQiOXFLKTQocFNmOFEpRzwiJCIrSDFXanchIik=

JCIrMT9zLTchIig=

P:=112; f:=qsAB(4,16,P); f:=f*(1-3/7)*(1-4/11); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiQ3Ig==

JCIrJjMmUSc+IiEjNQ==

JCIrPTdcXVYhIzY=

JCIrMHYjKUgiKSIiJA==

JCIrUSVHaSwiIiIk

JCIrLGInZmkiIiIl

JCIrKT1PJylHJSEiKQ==

NiQiTklzKlxuNHkxcz07dyN5aCRcJnkibypcdHojJCIrcCopW3c5ISIo

JCIrKWVfYCE+ISIo

P:=162; f2:=qsAB(4,16,P); f2:=f2*(1-3/7)*(1-4/11); HCCI42:=H*f2; %/8; 2*%%; log[2.](H*f2); primeprod(P); op(2,[%])+%%;

IiRpIg==

JCIrYkRHSyUqISM2

JCIrSDQjKkhNISM2

JCIrVlRhNGsiIiQ=

JCIreiwkPiwpIiIj

JCIrSCkzPkciIiIl

JCIrKillTGFVISIp

NiQiaW5xKUhDVXgqKil5a3F2MDdVdV56M25kalNbXDxQKnA7dmAkJCIrMk5nVz8hIig=

JCIrJzRQK1ojISIo

P:=352; f3:=qsAB(4,16,P); f3:=f3*(1-3/7)*(1-4/11); HCCI43:=H*f3; %/8; 2*%%; log[2.](H*f3); primeprod(P); op(2,[%])+%%;

IiRfJA==

JCIrNnBPMWEhIzY=

JCIrLzsmZic+ISM2

JCIrUkghUW4kIiIk

JCIrdU9EI2YlIiIj

JCIreWVnWnQiIiQ=

JCIrUTYvdVQhIik=

NiQiaHNxLkw4QChbMmQ7XkJISFctPylIJ0dKWElISEA3ejNCaXAveG96RDMzLWFYKWZ2JzNYZCNcdVtEJHlNdWddQDZ3X3gnKT1VY3FZOkUkIis+K2RrWSEiKA==

JCIrTFQoPjMmISIo

f10:=qsAB(4,16,2^16);

JCIrTjtRR1YhIzc=

f10:=f10*(1-3/7)*(1-4/11); H*f10; 2*%;

JCIrZXAmUmQiISM3

JCIrRm5GVEgiIiM=

JCIrYU1iIyllIiIj

f13:=f10*(16/19)^4; H*f13; 2*%;

JCIrXGY4OnohIzg=

JCIrLUs2ejkiIiM=

JCIrL2tBZUgiIiM=

f15:=f13*(19/21)^4; H*f15; 2*%;

JCIrdUwhUkkmISM4

JCIrXUhbNioqIiIi

JCIrIWYnSCMpPiIiIw==

f18:=f18*(21/24)^4; H*f18; 2*%;

JCIrYGZdP10hIzg=

JCIrJSlSKj1RKiIiIg==

JCIrKHp5aig9IiIj

f26:=f18*(24/32)^4; H*f26; 2*%;

JCIraSU+JillIiEjOA==

JCIrJSopKltvSCIiIg==

JCIrKXl6cCRmIiIi

f29:=f26*(24/35)^4; H*f29; 2*%;

JCIrPHYzN04hIzk=

JCIrbSs0amwiIiE=

JCIrOCE9RUoiIiIi

f34:=f29*(35/40)^4; H*f34; 2*%;

JCIrQjdzZT8hIzk=

JCIrLkg7WlEiIiE=

JCIrMWVLJXAoIiIh

f44:=f34*(40/50)^4; H*f44; 2*%;

JCIrSEBfSyUpISM6

JCIrRHp6djoiIiE=

JCIrXWVmXkoiIiE=

#64 bit multiplier H:=HCCI40; %/8; 2*%%; P:=16.;

JCIrJXBFYHonIiIl

JCIrbyRlVFwpIiIk

JCIrUmAxZjgiIiY=

JCIjOyIiIQ==

150*p50/3.2/10^9; # 64 bit reciprocal modulo primes <= 50 bit, sec

JCIrdSY0R18iISIk

# density and number after sieve with <=16 bit primes f10/f0; %*H;

JCIrTjtRR1YhIzc=

JCIrRm5GVEgiIiM=

# sieve events for <=16 bit primes 4*H*ln(16./ln(P));

JCIrVyNmVnclIiIm

# density and number after sieve with <=32 bit primes f26/f0; %*H;

JCIrQCZHJW9WISM4

JCIrJSopKltvSCIiIg==

# sieve events for <=32 bit primes 4*H*ln(32./ln(P));

JCIrZ1FVW20iIiY=

# sieve events for <=50 bit primes 4*H*ln(50./ln(P));

JCIrQzBcaHkiIiY=

%/0.8/10^9; # total sieve time in sec

JCIrYkonbyMpKiEiJQ==

#128 bit multiplier H:=HCCI41; %/8; 2*%%; P:=65.;

JCIrSG5pbzgiIiU=

JCIrNk15NTwiIiQ=

JCIrZU1EUEYiIiU=

JCIjbCIiIQ==

200*p50/3.2/10^9; # 128 bit reciprocal modulo primes <=50 bit, sec

JCIrbUZUST8hIiQ=

# density and number after sieve with <=16 bit primes f10/f1; %*H;

JCIrQToyXEAhIzY=

JCIrR25GVEgiIiM=

# sieve events for <=16 bit primes 4*H*ln(16./ln(P));

JCIrK0ttYnQiIiU=

# density and number after sieve with <=32 bit primes f26/f1; %*H;

JCIrel0mKm9AISM3

JCIrJiopKltvSCIiIg==

# sieve events for <=32 bit primes 4*H*ln(32./ln(P));

JCIrQy0uOjYiIiY=

# sieve events for <=50 bit primes 4*H*ln(50./ln(P));

JCIrMS9OZjgiIiY=

%/0.8/10^9; # total sieve time in sec

JCIrMyEpPSpwIiEiJQ==

#256 bit multiplier H:=HCCI42; %/8; 2*%%; P:=162.;

JCIrVlRhNGsiIiQ=

JCIreiwkPiwpIiIj

JCIrSCkzPkciIiIl

JCIkaSIiIiE=

300*p50/3.2/10^9; # 256 bit reciprocal modulo primes <=50 bit, sec

JCIrWyI+Yy8kISIk

# density and number after sieve with <=16 bit primes f10/f2; %*H;

JCIrJGUsKillJSEjNg==

JCIrRW5GVEgiIiM=

# sieve events for <=16 bit primes 4*H*ln(16./ln(P));

JCIrI0h6diRIIiIl

# density and number after sieve with <=32 bit primes f26/f2; %*H;

JCIrVCllOGolISM3

JCIrJCopKltvSCIiIg==

# sieve events for <=32 bit primes 4*H*ln(32./ln(P));

JCIrc0FvOVoiIiU=

# sieve events for <=50 bit primes 4*H*ln(50./ln(P));

JCIrQzUpKWVlIiIl

%/0.8/10^9; # total sieve time in sec

JCIrIUcsT0soISIm

#512 bit multiplier H:=HCCI43; %/8; 2*%%; P:=352.;

JCIrUkghUW4kIiIk

JCIrdU9EI2YlIiIj

JCIreWVnWnQiIiQ=

JCIkXyQiIiE=

500*p50/3.2/10^9; # 512 bit reciprocal modulo primes <=50 bit, sec

JCIrOT4ud10hIiQ=

# density and number after sieve with <=16 bit primes f10/f3; %*H;

JCIrOT4zMSEpISM2

JCIrRm5GVEgiIiM=

# sieve events for <=16 bit primes 4*H*ln(16./ln(P));

JCIrVFU4djkiIiU=

# density and number after sieve with <=32 bit primes f26/f3; %*H;

JCIreGE6ITMpISM3

JCIrJSopKltvSCIiIg==

# sieve events for <=32 bit primes 4*H*ln(32./ln(P));

JCIrKyhHUFwjIiIl

# sieve events for <=50 bit primes 4*H*ln(50./ln(P));

JCIrW3FiXEoiIiU=

%/0.8/10^9; # total sieve time in sec

JCIrNWolcCRSISIm

H*f44/f3*300/32^2/1.902321417; # SPU time in sec

JCIrNT8jb1UjISIi

%/24/3600/420; # time for all SPU in days

JCIrJCkzbihvJyEiKg==

# Cunningham chain I, length 5 f:=qsAB(5,18,64);

JCIrdnJmRT0hIzU=

f:=f*(1-3/7)*(1-5/11)*(1-11/17);

JCIrTWtSND8hIzY=

H:=HCCI5; H/8; H*f; 2*%;

JCIrRypRZ0ciIiIo

JCIrZydbdmciIiIn

JCIrTz87JWUjIiIm

JCIrc1NLb14iIiY=

P:=60; f1:=qsAB(5,18,P); f1:=f1*(1-3/7)*(1-5/11)*(1-11/17); HCCI51:=H*f1; %/8; 2*%%; log[2.](H*f1); primeprod(P); op(2,[%])+%%;

IiNn

JCIrNGlvKik+ISM1

JCIrSW8hKSk9IyEjNg==

JCIrKnkhKlsiRyIiJg==

JCIrJ1s4Jz1OIiIl

JCIreTp5SGMiIiY=

JCIrR3MrK1shIik=

NiQiN3EhUkVAYSxOZ0YjPiQiKyYqb09xcSEiKQ==

JCIrN3UuKD0iISIo

P:=155; f2:=qsAB(5,18,P); f2:=f2*(1-3/7)*(1-5/11)*(1-11/17); HCCI52:=H*f2; %/8; 2*%%; log[2.](H*f2); primeprod(P); op(2,[%])+%%;

IiRiIg==

JCIrWFpPcnMhIzY=

JCIrNW4wKip6ISM3

JCIrSyk0KEc1IiIm

JCIrIUgoKWVHIiIiJQ==

JCIrayc+dTAjIiIm

JCIrVkh5YVkhIik=

NiQiZ241PjRXbE5pTDsmb104KyMqKkdpQiEqKUd0PEo9KlxgPmBBJCIrK3Rscj4hIig=

JCIrJWZOclYjISIo

P:=348; f3:=qsAB(5,18,P); f3:=f3*(1-3/7)*(1-5/11)*(1-11/17); HCCI53:=H*f3; %/8; 2*%%; log[2.](H*f3); primeprod(P); op(2,[%])+%%;

IiRbJA==

JCIreC9TY04hIzY=

JCIrOEFKN1IhIzc=

JCIrL2VRSl0iIiU=

JCIrYkFCKkcnIiIk

JCIraHJGMTUiIiY=

JCIrMEBnXlghIik=

NiQiZXNJXlkqcHNiUHUkcGRmbCcpeUQzXE5oNk8kKSlITC9PbjcjeUV0byQqPlAqcFVYanReampGKilwXCd5KmYiM05sQWs3TClRZW5uJVw8JVwoJCIrKD0qNCFlJSEiKA==

JCIrKVJmXy4mISIo

P:=708; f4:=qsAB(5,18,P); f4:=f4*(1-3/7)*(1-5/11)*(1-11/17); HCCI54:=H*f4; %/8; 2*%%; log[2.](H*f4); primeprod(P); op(2,[%])+%%;

IiQzKA==

JCIrZGtVMj8hIzY=

JCIrZUNLM0EhIzc=

JCIrWicpKSpSRyIiJQ==

JCIrNGUpKlxOIiIk

JCIrJUh4KnpjIiIl

JCIrU100cFchIik=

NiQiYF1sSU1QJltYRjdPJ2VbRSg+cWVdUlhAZ0YsKVxpTDlYc0QneiVvQE06JUdsLW0mZSZwLmM9Z1gwOEsrVGJzXVE0N19eczJBMl8sKSplbDM1SlQsIlsvKCkqPWU4P1wnW29VWC5LcUtRJ28ieSYzPFlvZnFjInojR0pTMGEmb3ZNdj9QZSllVCE9eTd2ZmtCRFJpKmY0OkFWdFA6LDJ0eFk+JCIrOzRrNCgqISIo

JCIrVV1sOjUhIic=

P:=1445; f5:=qsAB(5,18,P); f5:=f5*(1-3/7)*(1-5/11)*(1-11/17); HCCI55:=H*f5; %/8; 2*%%; log[2.](H*f5); primeprod(P); op(2,[%])+%%;

IiVYOQ==

JCIrZ0EtPDchIzY=

JCIrZnUiKVE4ISM3

JCIrcTh4QDwiIiU=

JCIrN1VAX0AiIiQ=

JCIrU0ZhVk0iIiU=

JCIrIyllKm9SJSEiKQ==

NiQiZGBtIVJDTzVUaVRsPCI0X3hUIT5OKW9CIyp5cSt5WkJnXnBXYEI+d0pDZz1bKHoneXN2dDBhZUtJJXooeSMzPXlfRihHd1dPZjQkZWlZI2VoTFZRZCIzRDBTYCRwIylHcDY5PjpKVk1gMnlDUGM3VykpZiE0IilSZiZITjguSVtCKT1DTydcKysyWl5HcGdeUz4kcCFbIUdjI1JyJClRJWYoZVEhKkchM04jZV5eO28wRT9LUCU9SGdHOT4nb0lpeGJodmslKlJgbmg0U3kzbG04Nls8RkFnSiEpeVE/ITQnZTM9UWEnW1lkQiplcGJQZjsjb0JlVT1aUTAyb20tNjU7TGQhKSp6P1MpPSJ5ZFJ2TyMqeiYpSFxUUzwmbyFwWElOJj4kSHpvZkFbKWVKISkpPSVbRlM3IilwOCUzZnY6LEFKLyRlNVw6dyhHPi0sPk5TIiQiKzFmayQqPiEiJw==

JCIrbFtoUD8hIic=

P:=2855; f6:=qsAB(5,18,P); f6:=f6*(1-3/7)*(1-5/11)*(1-11/17); HCCI56:=H*f6; %/8; 2*%%; log[2.](H*f6); primeprod(P); op(2,[%])+%%;

IiViRw==

JCIrZSdSJ1J4ISM3

JCIrKClbPjkmKSEjOA==

JCIrMidlXDQiIiIl

JCIrZiMpcG84IiIk

JCIrOXMiKio9IyIiJQ==

JCIrZFRmSlYhIik=

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

JCIrJm8nZiozJSEiJw==

f10:=qsAB(5,18,2^16);

JCIrXSoqSCJcIiEjNw==

f10:=f10*(1-3/7)*(1-5/11)*(1-11/17); H*f10; 2*%;

JCIrc1FhUzshIzg=

JCIrI0cuKTRAIiIk

JCIra2xnPlUiIiQ=

f13:=f10*(16/19)^5; H*f13; 2*%;

JCIrZSNmdCVwISM5

JCIrYFdkTSopIiIj

JCIrIipbInB5IiIiJA==

f15:=f13*(19/21)^5; H*f15; 2*%;

JCIreSRHP0AlISM5

JCIrZ0Mkb1QmIiIj

JCIrI1xtTDMiIiIk

f18:=f15*(21/24)^5; H*f18; 2*%;

JCIrIypwUWdAISM5

JCIrcjxNeUYiIiM=

JCIrVU5vY2IiIiM=

f26:=f18*(24/32)^5; H*f26; 2*%;

JCIrKycqcEVeISM6

JCIrZV84JGYnIiIi

JCIrX3FpPTgiIiM=

f29:=f26*(32/35)^5; H*f29; 2*%;

JCIrbktGdkshIzo=

JCIrQCpHQEAlIiIi

JCIrVXlEQyUpIiIi

f34:=f29*(35/40)^5; H*f34; 2*%;

JCIrRHAiKno7ISM6

JCIraCZRLzsjIiIi

JCIrQXIoM0slIiIi

f44:=f34*(40/50)^5; H*f44; 2*%;

JCIrIXleWl0mISM7

JCIreV1LenEiIiE=

JCIrO10nZVQiIiIi

#128 bit multiplier H:=HCCI51; %/8; 2*%%; P:=60.;

JCIrKnkhKlsiRyIiJg==

JCIrJ1s4Jz1OIiIl

JCIreTp5SGMiIiY=

JCIjZyIiIQ==

200*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrbUZUST8hIiQ=

# density and number after sieve with <=16 bit primes f10/f1; %*H;

JCIrbTk6JlwoISM3

JCIrI0cuKTRAIiIk

# sieve events for <=16 bit primes 5*H*ln(16./ln(P));

JCIrWUdLPT4iIic=

# density and number after sieve with <=32 bit primes f26/f1; %*H;

JCIrTFtCVUIhIzg=

JCIrZF84JGYnIiIi

# sieve events for <=32 bit primes 5*H*ln(32./ln(P));

JCIrXycqKVEqRyIiJw==

# sieve events for <=50 bit primes 5*H*ln(50./ln(P));

JCIrIlE5P18kIiIn

%/0.8/10^9; # total sieve time in sec

JCIrd3peLVchIiQ=

#256 bit multiplier H:=HCCI52; %/8; 2*%%; P:=155.;

JCIrSyk0KEc1IiIm

JCIrIUgoKWVHIiIiJQ==

JCIrayc+dTAjIiIm

JCIkYiIiIiE=

300*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrWyI+Yy8kISIk

# density and number after sieve with <=16 bit primes f10/f2; %*H;

JCIrbjsjNDAjISM2

JCIrJUcuKTRAIiIk

# sieve events for <=16 bit primes 5*H*ln(16./ln(P));

JCIrJlJXI1FmIiIm

# density and number after sieve with <=32 bit primes f26/f2; %*H;

JCIrNC04NGshIzg=

JCIraF84JGYnIiIi

# sieve events for <=32 bit primes 5*H*ln(32./ln(P));

JCIrJio0Wy4mKiIiJg==

# sieve events for <=50 bit primes 5*H*ln(50./ln(P));

JCIrbCEpKil6NiIiJw==

%/0.8/10^9; # total sieve time in sec

JCIrImVzW1oiISIk

#512 bit multiplier H:=HCCI53; %/8; 2*%%; P:=348.;

JCIrL2VRSl0iIiU=

JCIrYkFCKkcnIiIk

JCIraHJGMTUiIiY=

JCIkWyQiIiE=

500*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrOT4ud10hIiQ=

# density and number after sieve with <=16 bit primes f10/f3; %*H;

JCIrVllHJD4lISM2

JCIrI0cuKTRAIiIk

# sieve events for <=16 bit primes 5*H*ln(16./ln(P));

JCIrZytASUQiIiY=

# density and number after sieve with <=32 bit primes f26/f3; %*H;

JCIrXjlTNTghIzc=

JCIrZV84JGYnIiIi

# sieve events for <=32 bit primes 5*H*ln(32./ln(P));

JCIrLGImUkYlIiIm

# sieve events for <=50 bit primes 5*H*ln(50./ln(P));

JCIrK29uJ1ImIiIm

%/0.8/10^9; # total sieve time in sec

JCIrK2clZXUnISIl

#1024 bit multiplier H:=HCCI54; %/8; 2*%%; P:=708.;

JCIrWicpKSpSRyIiJQ==

JCIrNGUpKlxOIiIk

JCIrJUh4KnpjIiIl

JCIkMygiIiE=

900*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrWHUmbzgqISIk

# density and number after sieve with <=16 bit primes f10/f4; %*H;

JCIrJ1w5Kkd1ISM2

JCIrJEcuKTRAIiIk

# sieve events for <=16 bit primes 5*H*ln(16./ln(P));

JCIrN2BgbDciIiY=

# density and number after sieve with <=32 bit primes f26/f4; %*H;

JCIrIXlOOksjISM3

JCIrZl84JGYnIiIi

# sieve events for <=32 bit primes 5*H*ln(32./ln(P));

JCIrdS4hKVxBIiIm

# sieve events for <=50 bit primes 5*H*ln(50./ln(P));

JCIrRWJfJClHIiIm

%/0.8/10^9; # total sieve time in sec

JCIrM3BTL08hIiU=

#2048 bit multiplier H:=HCCI55; %/8; 2*%%; P:=1445.;

JCIrcTh4QDwiIiU=

JCIrN1VAX0AiIiQ=

JCIrU0ZhVk0iIiU=

JCIlWDkiIiE=

1700*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrXjMmZXMiISIj

# density and number after sieve with <=16 bit primes f10/f5; %*H;

JCIrXnlPRDchIzU=

JCIrJUcuKTRAIiIk

# sieve events for <=16 bit primes 5*H*ln(16./ln(P));

JCIrU08rJXknIiIl

# density and number after sieve with <=32 bit primes f26/f5; %*H;

JCIrTFhGSFEhIzc=

JCIrZl84JGYnIiIi

# sieve events for <=32 bit primes 5*H*ln(32./ln(P));

JCIrXTM3djciIiY=

# sieve events for <=50 bit primes 5*H*ln(50./ln(P));

JCIrRklLZjsiIiY=

%/0.8/10^9; # total sieve time in sec

JCIrJXlgVDIjISIl

#4096 bit multiplier H:=HCCI56; %/8; 2*%%; P:=2855.;

JCIrMidlXDQiIiIl

JCIrZiMpcG84IiIk

JCIrOXMiKio9IyIiJQ==

JCIlYkciIiE=

3300*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrajU9XUwhIiM=

# density and number after sieve with <=16 bit primes f10/f6; %*H;

JCIrRlEkbyM+ISM1

JCIrJEcuKTRAIiIk

# sieve events for <=16 bit primes 5*H*ln(16./ln(P));

JCIrKG9pVyNRIiIl

# density and number after sieve with <=32 bit primes f26/f6; %*H;

JCIrNWROQGchIzc=

JCIrZ184JGYnIiIi

# sieve events for <=32 bit primes 5*H*ln(32./ln(P));

JCIrWCtJPnciIiU=

# sieve events for <=50 bit primes 5*H*ln(50./ln(P));

JCIrY0hFMTUiIiY=

%/0.8/10^9; # total sieve time in sec

JCIrJnBHeUQiISIl

H*f44/f6*300/64^2/1.925834177; # SPU time in sec

JCIrJjNuQnAjISIi

%/24/3600/420; # time for all SPU in days

JCIrQj5XPnUhIio=

# Cunningham chain I, length 6 f:=qsAB(6,18,64);

JCIrTT1GWjchIzU=

f:=f*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); H:=HCCI6; H/8; H*f; 2*%;

JCIrZ1IoKSk9KiEjNw==

JCIrKT1ebCZbIiIp

JCIrJikqKW9xZyIiKA==

JCIrdk9paVciIic=

JCIrXXRDRCopIiIn

P:=18; f:=qsAB(6,18,P); f:=f*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiM9

JCIiIiIiIQ==

JCIrdyN5ck8oISM2

JCIrVHkhemQkIiIo

JCIrLFtRc1ciIic=

JCIrI286ZTooIiIo

JCIrdmwqKilcJiEiKQ==

NiQiJzUwXiQiK3F6OicqPSEiKQ==

JCIrWFg6JlIoISIp

P:=58; f1:=qsAB(6,18,P); f1:=f1*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI61:=H*f1; %/8; 2*%%; log[2.](H*f1); primeprod(P); op(2,[%])+%%;

IiNl

JCIrUEAlKlI6ISM1

JCIrRUddTTYhIzY=

JCIrWjV4NGIiIic=

JCIrNFFAKClvIiIm

JCIrNFUmPjUiIiIo

JCIrejg0SF8hIik=

NiQiNUlaLyE+eCVlIiplSyQiKyFmLUBbJyEiKQ==

JCIrKFI+NjwiISIo

P:=155; f2:=qsAB(6,18,P); f2:=f2*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI62:=H*f2; %/8; 2*%%; log[2.](H*f2); primeprod(P); op(2,[%])+%%;

IiRiIg==

JCIrPyopPi9UISM2

JCIrOGxqQkkhIzc=

JCIrXVhXbzkiIic=

JCIrKW9iYiQ9IiIm

JCIrKyIqKW8kSCIiJw==

JCIrQDVLUV0hIik=

NiQiZ241PjRXbE5pTDsmb104KyMqKkdpQiEqKUd0PEo9KlxgPmBBJCIrK3Rscj4hIig=

JCIrLSUqW3ZDISIo

P:=345; f3:=qsAB(6,18,P); f3:=f3*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI63:=H*f3; %/8; 2*%%; log[2.](H*f3); primeprod(P); op(2,[%])+%%;

IiRYJA==

JCIraUMicHciISM2

JCIrNmZyLDghIzc=

JCIrYSpcPUsnIiIm

JCIrVUNKLXoiIiU=

JCIrIioqcFZFIiIiJw==

JCIrN1N0O1whIik=

NiQiY3MhemBrPWtSK2YoKWYvP144OHJfdyVvVS9XPUZuVDIkKVI/Wyk+Vz1rJGZWXEhBPyYqKSpSIyl6ZyNvalBMMDBaZFRAWkQ1Y2YvKGZAJCIrbzdyJlwlISIo

JCIrcFlRKClcISIo

P:=700; f4:=qsAB(6,18,P); f4:=f4*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI64:=H*f4; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiQrKA==

JCIreF54NSkpISM3

JCIrW14wIlwnISM4

JCIrZlRUX0oiIiY=

JCIrKnA8MCVSIiIl

JCIrPSRHW0knIiIm

JCIrdmwqKilcJiEiKQ==

NiQiXV1sSUNuOV80Y28kRyhRYjROVDshR1x3Q2FAWiVcKD0/JFsoUTNFTS1QIz1EXTMoKnlVUClwSF96W3JKeSNmNUxgP3ghKVx3VEd0MmhfQDBdXWQ1U0hVM0ckKkdMbzhwazpMODVoVU0oXD9RIWZkZXV1I3kzSTwyIkdkUnk+UHVhUHVQQ1goZXFMOiFcQHQ3XTY+aTo3Wi9ZSiI0VnJ4IyQiKzQjM15oKiEiKA==

JCIrKHkrbCwiISIn

P:=1445; f5:=qsAB(6,18,P); f5:=f5*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI65:=H*f5; %/8; 2*%%; log[2.](H*f5); primeprod(P); op(2,[%])+%%;

IiVYOQ==

JCIrJjNFK3olISM3

JCIrN3cqKUdOISM4

JCIrKj1GUXIiIiIm

JCIrJylSR1VAIiIl

JCIreVZsRk0iIiY=

JCIrKFxAJUdaISIp

NiQiZGBtIVJDTzVUaVRsPCI0X3hUIT5OKW9CIyp5cSt5WkJnXnBXYEI+d0pDZz1bKHoneXN2dDBhZUtJJXooeSMzPXlfRihHd1dPZjQkZWlZI2VoTFZRZCIzRDBTYCRwIylHcDY5PjpKVk1gMnlDUGM3VykpZiE0IilSZiZITjguSVtCKT1DTydcKysyWl5HcGdeUz4kcCFbIUdjI1JyJClRJWYoZVEhKkchM04jZV5eO28wRT9LUCU9SGdHOT4nb0lpeGJodmslKlJgbmg0U3kzbG04Nls8RkFnSiEpeVE/ITQnZTM9UWEnW1lkQiplcGJQZjsjb0JlVT1aUTAyb20tNjU7TGQhKSp6P1MpPSJ5ZFJ2TyMqeiYpSFxUUzwmbyFwWElOJj4kSHpvZkFbKWVKISkpPSVbRlM3IilwOCUzZnY6LEFKLyRlNVw6dyhHPi0sPk5TIiQiKzFmayQqPiEiJw==

JCIrQCwkNC8jISIn

P:=2850; f6:=qsAB(6,18,P); f6:=f6*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI66:=H*f6; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiVdRw==

JCIrJSlSLyl5IyEjNw==

JCIrMjwrYT8hIzg=

JCIrSVdPdioqIiIl

JCIrYTAjcEMiIiIl

JCIrJylHMiYqPiIiJg==

JCIrdmwqKilcJiEiKQ==

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

JCIrY016KjMlISIn

P:=5735; f7:=qsAB(6,18,P); f7:=f7*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); HCCI67:=H*f7; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiVOZA==

JCIrY2JiKHAiISM3

JCIrVCU+MUQiISM4

JCIrS3RwdGciIiU=

JCIrbDs3I2YoIiIk

JCIrbSVSWkAiIiIm

JCIrdmwqKilcJiEiKQ==

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

JCIrI3ooeiI9KSEiJw==

f10:=qsAB(6,18,2^16);

JCIrb0k1Y1EhIzg=

f10:=f10*(1-3/7)*(1-6/11)*(1-14/17)/(1-6/17)*(1-5/31)/(1-6/31); H*f10; 2*%;

JCIrdilmMyVHISM5

JCIrUyJ5J3o4IiIl

JCIrIUdjJGZGIiIl

f13:=f10*(16/19)^6; H*f13; 2*%;

JCIrdSw0ODUhIzk=

JCIrKUdDLCNcIiIk

JCIrdyZbLSUpKiIiJA==

f15:=f13*(19/21)^6; H*f15; 2*%;

JCIrK0w8ZGIhIzo=

JCIrZidwKSlwIyIiJA==

JCIrPSRSeFImIiIk

f18:=f15*(21/24)^6; H*f18; 2*%;

JCIraUwuJVwjISM6

JCIrcCtDNjciIiQ=

JCIrUSxbQUMiIiQ=

f26:=f18*(24/32)^6; H*f26; 2*%;

JCIrZE4lKVFXISM7

JCIrJjRaZDojIiIj

JCIrIT4lXDZWIiIj

f29:=f26*(32/35)^6; H*f29; 2*%;

JCIrdlp2I2YjISM7

JCIrR1k9ZjciIiM=

JCIrYyNwJD1EIiIj

f34:=f29*(35/40)^6; H*f34; 2*%;

JCIrMGloajYhIzs=

JCIrajs7XmMiIiI=

JCIrTEJCSTYiIiM=

f44:=f34*(40/50)^6; H*f44; 2*%;

JCIraytOXUkhIzw=

JCIrQiI9OVsiIiIi

JCIrWWkkRydIIiIi

#128 bit multiplier H:=HCCI61; %/8; 2*%%; P:=58.;

JCIrWjV4NGIiIic=

JCIrNFFAKClvIiIm

JCIrNFUmPjUiIiIo

JCIjZSIiIQ==

200*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrbUZUST8hIiQ=

# density and number after sieve with <=16 bit primes f10/f1; %*H;

JCIrO3IwL0QhIzc=

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrNiQ9TGAlIiIo

# density and number after sieve with <=32 bit primes f26/f1; %*H;

JCIrWSMqZTdSISM5

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrb3d3Q28iIig=

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIrQzo4KyQpIiIo

%/0.8/10^9; # total sieve time in sec

JCIrU2teUDUhIiI=

#256 bit multiplier H:=HCCI62; %/8; 2*%%; P:=155.;

JCIrXVhXbzkiIic=

JCIrKW9iYiQ9IiIm

JCIrKyIqKW8kSCIiJw==

JCIkYiIiIiE=

300*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrWyI+Yy8kISIk

# density and number after sieve with <=16 bit primes f10/f2; %*H;

JCIrU3NdJlIqISM3

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrTFc+PDUiIig=

# density and number after sieve with <=32 bit primes f26/f2; %*H;

JCIrMiFbIW85ISM4

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrYUwhemkiIiIo

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIrcz82QD8iIig=

%/0.8/10^9; # total sieve time in sec

JCIrITQhUkVEISIj

#512 bit multiplier H:=HCCI63; %/8; 2*%%; P:=345.;

JCIrYSpcPUsnIiIm

JCIrVUNKLXoiIiU=

JCIrIioqcFZFIiIiJw==

JCIkWCQiIiE=

500*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrOT4ud10hIiQ=

# density and number after sieve with <=16 bit primes f10/f3; %*H;

JCIrOGlSIz0jISM2

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrSVhoP1EiIic=

# density and number after sieve with <=32 bit primes f26/f3; %*H;

JCIrJjMlKio0TSEjOA==

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrOyEpelxrIiIn

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIrcVNoVSIpIiIn

%/0.8/10^9; # total sieve time in sec

JCIrZm4jeSwiISIj

#1024 bit multiplier H:=HCCI64; %/8; 2*%%; P:=700.;

JCIrZlRUX0oiIiY=

JCIrKnA8MCVSIiIl

JCIrPSRHW0knIiIm

JCIkKygiIiE=

900*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrWHUmbzgqISIk

# density and number after sieve with <=16 bit primes f10/f4; %*H;

JCIrKFJ3bFAlISM2

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrJFsmKSopbyIiIic=

# density and number after sieve with <=32 bit primes f26/f4; %*H;

JCIrQjFTUW8hIzg=

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrdncuK0kiIic=

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIrV247V1EiIic=

%/0.8/10^9; # total sieve time in sec

JCIrSSUzXyFbISIk

#2048 bit multiplier H:=HCCI65; %/8; 2*%%; P:=1445.;

JCIrKj1GUXIiIiIm

JCIrJylSR1VAIiIl

JCIreVZsRk0iIiY=

JCIlWDkiIiE=

1700*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrXjMmZXMiISIj

# density and number after sieve with <=16 bit primes f10/f5; %*H;

JCIrO2RGXSEpISM2

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrT0lDLiIpIiIm

# density and number after sieve with <=32 bit primes f26/f5; %*H;

JCIrImVieUQiISM3

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrJipcM0I6IiIn

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIrdy4rIyk+IiIn

%/0.8/10^9; # total sieve time in sec

JCIrcS9deEMhIiQ=

#4096 bit multiplier H:=HCCI66; %/8; 2*%%; P:=2850.;

JCIrSVdPdioqIiIl

JCIrYTAjcEMiIiIl

JCIrJylHMiYqPiIiJg==

JCIlXUciIiE=

3300*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrajU9XUwhIiM=

# density and number after sieve with <=16 bit primes f10/f6; %*H;

JCIrXWEzJFEiISM1

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrZE1NIz0lIiIm

# density and number after sieve with <=32 bit primes f26/f6; %*H;

JCIrPDUyaEAhIzc=

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrJyozKTRMKSIiJg==

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIreTFAKzYiIic=

%/0.8/10^9; # total sieve time in sec

JCIrW0xFdjghIiQ=

#8192 bit multiplier H:=HCCI67; %/8; 2*%%; P:=5735.;

JCIrS3RwdGciIiU=

JCIrbDs3I2YoIiIk

JCIrbSVSWkAiIiIm

JCIlTmQiIiE=

6500*p50/3.2/10^9; # reciprocal modulo primes <=50 bit, sec

JCIrKVtUKSlmJyEiIw==

# density and number after sieve with <=16 bit primes f10/f7; %*H;

JCIrQEFjckEhIzU=

JCIrUyJ5J3o4IiIl

# sieve events for <=16 bit primes 6*H*ln(16./ln(P));

JCIrOkFaUkEiIiY=

# density and number after sieve with <=32 bit primes f26/f7; %*H;

JCIrc2ZKXE4hIzc=

JCIrJjRaZDojIiIj

# sieve events for <=32 bit primes 6*H*ln(32./ln(P));

JCIrQD5YbFoiIiY=

# sieve events for <=50 bit primes 6*H*ln(50./ln(P));

JCIrJ2Y+PVInIiIm

%/0.8/10^9; # total sieve time in sec

JCIrJlx1KCopeiEiJQ==

H*f44/f7*300/128^2/2.373951103; # SPU time in sec

JCIrXFRqVTYhIiI=

%/24/3600/420; # time for all SPU in days

JCIrK016W0ohIio=

# Cunningham chain II, length 2 + twinprime qsAB(2,16,1000000);

JCIrSSMqUTRXISM2

q2:=%*(ln(1000000.)/(50*ln(2.)))^2;

JCIrS28jbysoISM3

qsAB(3,16,1000000);

JCIrWiVmMisqISM3

q3:=%*(ln(1000000.)/(50*ln(2.)))^3;

JCIrIlJlOnEmISM4

expval:=29.62739122*q3/q2; # Expected number of twins/Cullens

JCIrV1gjM1QjISIq

H:=2.^35; q3*H*260/expval; # SPU time in sec

JCIrUFEoZlYkIiIi

JCIrd1t3N0AiIiE=

%/24/3600/420; # time for all SPU in days

JCIrOE9AQWUhIik=

# Cunningham chain II, length 3 f:=qsAB(3,4,64); H:=2.^43; H/8; H*f; 2*%;

JCIrITMjPVZSISM2

JCIrQUk0J3opIiIk

JCIrRzteKjQiIiIk

JCIrUSdmJW9NIiIj

JCIrdyM+cCRwIiIj

P:=20; f:=qsAB(3,4,P); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiM/

JCIreUEieicpKSEjNg==

JCIrSiIpSCt5IiIj

JCIra0VQXSgqIiIi

JCIrRSdmK2MiIiIk

JCIrSlFaXVIhIik=

NiQiKCFwKnAqJCIrQDImNEsjISIp

JCIrX1hVcmkhIik=

P:=72; f:=qsAB(3,4,P); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiNz

JCIrZidvdWckISM2

JCIrISpIO3RKIiIj

JCIrUVBYbVIiIiI=

JCIrISlmS1lqIiIj

JCIrbklyP1EhIik=

NiQiPCFSOnUnNCcqKXBFLCQzJXpiJCIrZ1UtJikpKSEiKQ==

JCIrTFBkcTchIig=

P:=165; f:=qsAB(3,4,P); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiRsIg==

JCIrR28nej4jISM2

JCIrbz9OTD4iIiM=

JCIrJjMhcDtDIiIi

JCIrT1RxbVEiIiM=

JCIrVThCXFAhIik=

NiQiW281KW9nJik+ajExYywlUWxsSU1oTE4rakIhZjsmZigqPkE6bWQkIisqeSE0PUAhIig=

JCIrQlIsJFwjISIo

P:=358; f:=qsAB(3,4,P); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

IiRlJA==

JCIrRCVwUVkiISM2

JCIrakpqKEciIiIj

JCIrYTlhNDsiIiI=

JCIrRWpFdkQiIiM=

JCIrb0lmIXAkISIp

NiQianM1MWkwZyYpSHUlXGgqKj5TTmlva0sxVyYqXFdTOzZJLl1ud2QoZihIMTpgTXB2YWlbaTohKXllcHEqKVt5V1VrIiplbkNuSmcjcCI0KClmSyMqJCIral8/XFohIig=

JCIrcVhFPV4hIig=

f:=qsAB(3,4,2^19); H*f; 2*%;

JCIrKXlLJEc4ISM3

JCIreFFUbzYiIiI=

JCIrYXgjb0wjIiIi

f:=f*(19/21)^3; H*f; 2*%;

JCIrL3kxUSkqISM4

JCIrY2ZsYCcpIiIh

JCIrIj5KMnQiIiIi

f:=f*(21/24)^3; H*f; 2*%;

JCIrSW90IWYnISM4

JCIrQ01GKHomIiIh

JCIrJm9hJWY2IiIi

f:=f*(24/35)^3; H*f; 2*%;

JCIrWUUtREAhIzg=

JCIrKG8qPXA9IiIh

JCIrdSR6JFFQIiIh

f:=f*(35/40)^3; H*f; 2*%;

JCIrYiIqZkI5ISM4

JCIrZjVAXzciIiE=

JCIrPUBVL0QiIiE=

f:=f*(40/50)^3; H*f; 2*%;

JCIrdXcjKSlHKCEjOQ==

JCIrQzFLNmshIiI=

JCIrRFRFI0ciIiIh

H*f*300/16^2/2.380149958; # SPU time in sec

JCIrN2RqY0ohIiI=

%/24/3600/420; # time for all SPU in days

JCIrKnpUKSlwKSEiKg==

# Cunningham chain II, length 4 f:=qsAB(4,6,64); f:=f*(1-3/7)/(1-4/7); H:=2.^49; H/8; H*f; 2*%;

JCIrQjB6LVEhIzY=

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P:=16; f:=qsAB(4,6,P); f:=f*(1-3/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=70; f:=qsAB(4,6,P); f:=f*(1-3/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=165; f:=qsAB(4,6,P); f:=f*(1-3/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=352; f:=qsAB(4,6,P); f:=f*(1-3/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=718; f:=qsAB(4,6,P); f:=f*(1-3/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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f:=qsAB(4,6,2^19); f:=f*(1-3/7)/(1-4/7); H*f; 2*%;

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f:=f*(19/21)^4; H*f; 2*%;

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f:=f*(21/24)^4; H*f; 2*%;

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f:=f*(24/35)^4; H*f; 2*%;

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f:=f*(35/40)^4; H*f; 2*%;

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f:=f*(40/50)^4; H*f; 2*%;

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H*f*300/64^2/1.731884327; # SPU time in sec

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%/24/3600/420; # time for all SPU in days

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# Cunningham chain II, length 5 f:=qsAB(5,6,64); f:=f*(1-2/7)/(1-4/7); H:=2.^54; H/8; H*f; 2*%;

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P:=12; f:=qsAB(5,6,P); f:=f*(1-2/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=65; f:=qsAB(5,6,P); f:=f*(1-2/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=162; f:=qsAB(5,6,P); f:=f*(1-2/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=348; f:=qsAB(5,6,P); f:=f*(1-2/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=708; f:=qsAB(5,6,P); f:=f*(1-2/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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P:=1445; f:=qsAB(5,6,P); f:=f*(1-2/7)/(1-4/7); H*f; %/8; 2*%%; log[2.](H*f); primeprod(P); op(2,[%])+%%;

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f:=qsAB(5,6,2^19); f:=f*(1-2/7)/(1-4/7); H*f; 2*%;

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f:=f*(19/21)^5; H*f; 2*%;

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f:=f*(21/24)^5; H*f; 2*%;

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f:=f*(24/35)^5; H*f; 2*%;

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f:=f*(35/40)^5; H*f; 2*%;

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f:=f*(40/50)^5; H*f; 2*%;

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H*f*300/128^2/2.132358865; # SPU time in sec

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%/24/3600/420; # time for all SPU in days

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# Cunningham chain II, length 6 f:=qsAB(6,6,64); f:=f*(1-1/7)/(1-4/7)*(1-25/31)/(1-26/31); H:=2.^58; H/8; H*f; 2*%;

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f:=qsAB(6,6,68); f:=f*(1-1/7)/(1-4/7)*(1-25/31)/(1-26/31); H*f; 2*%;

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f:=qsAB(6,6,2^19); f:=f*(1-1/7)/(1-4/7)*(1-25/31)/(1-26/31); H*f; 2*%;

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f:=f*(19/21)^6; H*f; 2*%;

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f:=f*(21/24)^6; H*f; 2*%;

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f:=f*(24/35)^6; H*f; 2*%;

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f:=f*(35/40)^6; H*f; 2*%;

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f:=f*(40/50)^6; H*f; 2*%;

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H*f*300/256^2/1.927056039; # SPU time in sec

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%/24/3600/420; # time for all SPU in days

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# # This triviality makes a list of the differences # between odd primes up to a given limit. The # half of the differences is stored. The first # item is 1=(5-3)/2. # primes:=proc(N) local p,pp,L; L:=[]; pp:=3; for p from 5 while p<=N by 2 do if isprime(p) then L:=[op(L),(p-pp)/2]; pp:=p; fi; od; L end;

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L:=primes(1000);

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save(L,"primediffs"); read("primediffs");

> L := [1, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 3, 1, 3, 2, 1, 3, 2, 3, 4, 2, > 1, 2, 1, 2, 7, 2, 3, 1, 5, 1, 3, 3, 2, 3, 3, 1, 5, 1, 2, 1, 6, 6, 2, 1, 2, 3, > 1, 5, 3, 3, 3, 1, 3, 2, 1, 5, 7, 2, 1, 2, 7, 3, 5, 1, 2, 3, 4, 3, 3, 2, 3, 4, > 2, 4, 5, 1, 5, 1, 3, 2, 3, 4, 2, 1, 2, 6, 4, 2, 4, 2, 3, 6, 1, 9, 3, 5, 3, 3, > 1, 3, 5, 3, 3, 1, 3, 3, 2, 1, 6, 5, 1, 2, 3, 3, 1, 6, 2, 3, 4, 5, 4, 5, 4, 3, > 3, 2, 4, 3, 2, 4, 2, 7, 5, 6, 1, 5, 1, 2, 1, 5, 7, 2, 1, 2, 7, 2, 1, 2, 10, 2, > 4, 5, 4, 2, 3, 3, 7, 2, 3, 3, 4, 3];

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