{VERSION 7 1 "Linux" "7.1" } {USTYLETAB {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "MS Serif" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1 " -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 12 40 120 40 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "MS Serif" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Norm al" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 } 1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "MS Serif" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Orde red List 4" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Wa rning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "He ading 1" -1 3 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 2" -1 204 1 {CSTYLE "" -1 -1 "Times " 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 } {CSTYLE "Equation Label" -1 200 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Page Number" -1 33 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 202 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "MS Serif" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{PSTYLE "" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 12 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 203 66 "Sz\303\241m\303\255t\303 \263g\303\251pes sz\303\241melm\303\251let" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 18 "J\303\241rai Antal" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 68 "Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\2 41lnak" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 59 "1. A pr\303\255mek el oszl\303\241sa, szit\303\241l\303\241s" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "restart; with(numtheory );" }}{PARA 11 "" 1 "" {XPPMATH 20 "7QI&GIgcdG6\"I)bigomegaGF$I&cfracG F$I)cfracpolGF$I+cyclotomicGF$I)divisorsGF$I)factorEQGF$I*factorsetGF$ I'fermatGF$I)imagunitGF$I&indexGF$I/integral_basisGF$I)invcfracGF$I'in vphiGF$I*issqrfreeGF$I'jacobiGF$I*kroneckerGF$I'lambdaGF$I)legendreGF$ I)mcombineGF$I)mersenneGF$I(migcdexGF$I*minkowskiGF$I(mipolysGF$I%mlog GF$I'mobiusGF$I&mrootGF$I&msqrtGF$I)nearestpGF$I*nthconverGF$I)nthdeno mGF$I)nthnumerGF$I'nthpowGF$I&orderG%*protectedGI)pdexpandGF$I$phiGF$I #piGF$I*pprimrootGF$I)primrootGF$I(quadresGF$I+rootsunityGF$I*safeprim eGF$I&sigmaGF$I*sq2factorGF$I(sum2sqrGF$I$tauGF$I%thueGF$" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "1.1. A pr" }{TEXT 206 8 "\303\255" }{TEXT 206 3 "msz" }{TEXT 206 8 "\303\241" }{TEXT 206 2 "mt" }{TEXT 206 8 " \303\251" }{TEXT 206 4 "tel." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "[i$i=1..20]; evalf(map(i->lo g[2](mersenne([i])+1),%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "76\"\"\"\" \"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5\"#6\"#7\"#8\"#9\"#:\"#;\"#< \"#=\"#>\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "76$\"\"#\"\"!$\"\"$F%$\" \"&F%$\"\"(F%$\"#8F%$\"#F%$\"#JF%$\"#hF%$\"#*)F%$\"$2\"F%$\"$F \"F%$\"$@&F%$\"$2'F%$\"%z7F%$\"%.AF%$\"%\"G#F%$\"% " 0 "" {MPLTEXT 1 0 31 "primeprod:=proc(n) loca l p,i;\n" }{MPLTEXT 1 0 9 " p:=1;\n" }{MPLTEXT 1 0 57 " for i from 2 to n do if isprime(i) then p:=p*i fi od;\n" }{MPLTEXT 1 0 17 " p,log [2.](p);\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6 #I\"nG6\"6$I\"pGF%I\"iGF%F%F%C%>F'\"\"\"?(F(\"\"#F+F$I%trueG%*protecte dG@$-I(isprimeG6$F/I(_syslibGF%6#F(>F'*&F'F+F(F+6$F'-&I$logGF36#$F-\" \"!6#F'F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "primeprod( 16);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"&I+$$\"+&o6u[\"!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "primeprod(32);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$\"-I,\\g0?$\"+ZY_aP!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "primeprod(64);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$\"9qK)4(pSf8Q)G<\"$\"+H1Wjw!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "primeprod(128);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\" RIxC&)ekO^/E!*>TW4*=OILRpZ9S$\"+1wd9;!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "primeprod(256);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$ \"`qI-UMKu+___Jq!)yO]\")*3oeZC9\"3#4;f'=!)3J8n5G_jIB([k3z\"4LmU'$\"+E( o([L!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "primeprod(512); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"_xIS9@`?a@4U])\\$Hst5%*=2ND(p9 \\0,$pm(=fxn!47%*p\"fe(p8'=a-MH=d)o52#)zJz!)HI&))yUx2GG)zmIC=O;_4IPT%* =*f0Gr\\RFIDuSYb))o>(G\"3k>$$\"+'zKg-(!\"(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "primeprod(1024);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 $\"gelIlj(GW\\0gA6O-5'fe](oFmg9w0p%oe`xeI\">.X$)[8O(RK(>f>T()3+f_iLM[o MAEdzXn!RKoM04o0C%*eXwC62)4?J.=mjwUMcl3DB]rErN&))ohxr+jXOq@L[SN>#z1876 B0#GD;LQ])egsxJ\")Qv(fEI3()=(3)f)3%p,VZG4$z$*QJ'[@d)3;jG(e\">IWiG(=d9= Sy+\\Stu+*)o&GlosXuGS?f&yi_!=(p=WaD$3#$\"+O@_>9!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "primeprod(2048);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"j`n!>!Gvbv@I#y:H7Lw^0fGyoDUyOC#yvG[5F`$=[l[zOhN[*z)HJ #zq()eaU')oC=C+2%\\pO&*Hjyp-Ucff],)zL?vgXLcg=ET6r(QUO+@RI(H:.?&zbE$\\! 3zz!=8\"G#[/yJpQ15$eYzDBjMGrX5rb#*y&o.HcJ%*er-Z@[7V!>ZBr2ul#fNU;MY!p&p $GJO;X`()G)42WgF/+!3@AO%f=^>)>`vR2?]_1Ce1W023fCV&\\CCg_R?;8z:cVn+5ra#= C!zpI+8X[%=JBOStXW=V*yybU#p4N-t)zFU[\"z$zi%*Hkv(y4zz8hgqnO9!4]_LflCF \\fI(*)fU(*)\\xzu!Ro93\\l4\\uoB*G`NAwk5x\\)Rbj*H=Qc.$Q\\jiI)R&zsqAxHny \"pH,pMAu'>4nPt__!o\"[^[G(=\"y$yiE?=WV)o;**4CeM$\"+j8[kG!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "pd16:=1/ln(2.)/16; # approximate density of primes <= 16 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+1S%o,*!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "p16:=2.^16/ln(2.)/16; # approximate number of primes <=16 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+)))y#4 f!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "pd32:=1/ln(2.)/32; # approximate density of primes <=32 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+.?U3X!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "p32:=2.^32/ln(2.)/32; # approximate number of primes <=32 bit" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+1DNO>!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "pd35:=1/ln(2.)/35; # approximate density of prime s <=35 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Je)>7%!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "p35:=2.^35/ln(2.)/35; # approximate number of primes <=35 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ZNI;9 \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "pd40:=1/ln(2.)/40; # approximate density of primes <=40 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+-wt1O!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "p40:=2.^40/ln(2.)/40; # approximate number of primes <=40 bit" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+L*\\c'R\"\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 59 "pd50:=1/ln(2.)/50; # approximate density of pr imes <=50 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+#3!R&)G!#6" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "p50:=2.^50/ln(2.)/50; # appr oximate number of primes <=50 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +D/m[K\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "pd64:=1/ln(2 .)/64; # approximate density of primes <=64 bit" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+-5@aA!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "p64:=2.^64/ln(2.)/64; # approximate number of primes <=64 bit" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+V`GeT\"\")" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "1.2. K" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "rd" }{TEXT 206 8 "\303\251" }{TEXT 206 10 " s: zeta gy" }{TEXT 206 8 "\303\266" }{TEXT 206 4 "kei." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "1.3. K" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "rd" }{TEXT 206 23 "\303\251s: \317\200(x)." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 11 "1.4. Ikerpr" }{TEXT 206 8 "\303\255" }{TEXT 206 4 "mek." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "1.5. K" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "rd" }{TEXT 206 24 "\303\251s: \317\200_2(x)" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "1.6. K" }{TEXT 206 8 "\303\251 " }{TEXT 206 2 "rd" }{TEXT 206 8 "\303\251" }{TEXT 206 12 "s: az ikerp r" }{TEXT 206 8 "\303\255" }{TEXT 206 18 "mek reciprokainak " }{TEXT 206 8 "\303\266" }{TEXT 206 7 "sszege." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "1.7. Sejt" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "s." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 57 "# This procedure approximate Cs calculatin g the product\n" }{MPLTEXT 1 0 23 "# for primes below x.\n" }{MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 42 "Cs:=proc(s::posint, x::posint) local P,p;\n" }{MPLTEXT 1 0 25 "P:=1.; p:=nextprime(s);\n" }{MPLTEXT 1 0 58 "while pF,$\"\" \"\"\"!>F--I*nextprimeG6$F(I(_syslibGF&6#F%?(F&F1F1F&2F-F*C$>F,*(F,F1, &F1F1*&F%F1F-!\"\"F@F1),&F1F1*$F-F@F@F%F@>F--F56#F-F,F&F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Cs(2,10); Cs(2,100); Cs(2,10 00); Cs(2,10000); Cs(2,100000);\n" }{MPLTEXT 1 0 19 "Cs2:=Cs(2,1000000 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+)\\Pf$o!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Y3x8m!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ZuX-m! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+uHo,m!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+GMi,m!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+m$=;g'! #5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Cs(3,10); Cs(3,100); \+ Cs(3,1000); Cs(3,10000); Cs(3,100000);\n" }{MPLTEXT 1 0 19 "Cs3:=Cs(3, 1000000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+q.7*3(!#5" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+]'RpQ'!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +?s3aj!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++1&=N'!#5" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+I)y;N'!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +/[m^j!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Cs(4,10); Cs(4 ,100); Cs(4,1000); Cs(4,10000); Cs(4,100000);\n" }{MPLTEXT 1 0 19 "Cs4 :=Cs(4,1000000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+.F'o(Q!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+/4L4J!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+enHxI!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Q*H^2$! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+HO'\\2$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+?,&\\2$!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Cs(5,10); Cs(5,100); Cs(5,1000); Cs(5,10000); Cs(5,100000);\n" } {MPLTEXT 1 0 19 "Cs5:=Cs(5,1000000);" }}{PARA 11 "" 1 "" {XPPMATH 20 " $\"+A:Tvh!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+%*RrvT!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+@#oR5%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+s7:*4%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+> " 0 "" {MPLTEXT 1 0 61 "Cs(6,10); Cs(6,100); Cs(6,1000); Cs(6,10000); Cs(6 ,100000);\n" }{MPLTEXT 1 0 19 "Cs6:=Cs(6,1000000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+*QBBg$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+r'f\" >>!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+?*4(p=!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+?yTm=!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fa;m =!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+l[9m=!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Cs(7,10); Cs(7,100); Cs(7,1000); Cs(7,10000 ); Cs(7,100000);\n" }{MPLTEXT 1 0 19 "Cs7:=Cs(7,1000000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +'[LF%Q!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+$RoUq$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Op8&p$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+$GPWp$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+$>!Q%p$!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Cs(8,10); Cs(8,100); Cs(8,10 00); Cs(8,10000); Cs(8,100000);\n" }{MPLTEXT 1 0 19 "Cs8:=Cs(8,1000000 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+O>(*\\C!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3() \\KB!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+CB!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "evalf(9*exp(-2*ga mma)*Cs(3,10));\n" }{MPLTEXT 1 0 35 "evalf(9*exp(-2*gamma)*Cs(3,100)); \n" }{MPLTEXT 1 0 36 "evalf(9*exp(-2*gamma)*Cs(3,1000));\n" }{MPLTEXT 1 0 37 "evalf(9*exp(-2*gamma)*Cs(3,10000));\n" }{MPLTEXT 1 0 38 "evalf (9*exp(-2*gamma)*Cs(3,100000));\n" }{MPLTEXT 1 0 37 "evalf(9*exp(-2*ga mma)*Cs(3,1000000));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+\\hF6?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+(He?\"=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Lwt-=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+vI5-=! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+TV0-=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+i.0-=!\"*" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 6 " 1.8. P" }{TEXT 206 8 "\303\251" }{TEXT 206 4 "lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "# Twin prim e, old" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f1:=h->(3.+30*h)* 2.^38880.-1;\n" }{MPLTEXT 1 0 18 "f2:=f1+2; f2(1);\n" }{MPLTEXT 1 0 28 "g:=h->1/ln(f1(h))/ln(f2(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6# I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"\"$\"\"!\"\"\",$*&\"#IF/ F$F/F/F/F/)$\"\"#F.$\"&!))QF.F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I#f1G6\"\"\"\"\"\"#F%" }}{PARA 11 "" 1 "" {XPPMATH 20 " $\"+6,nqO\"&'p6" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)ope ratorGF%I&arrowGF%F%*&-I#lnG6$%*protectedGI(_syslibGF%6#-I#f1GF%F#!\" \"-F+6#-I#f2GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^27; H/6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*Gx@M\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+gE`X=!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "Cf1f2:=C2*(1-1/3)^2/(1-2/3)* (1-1/5)^2/(1-2/5)/(1-1/2)^2/(1-1/3)^2/(1-1/5)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#?\"\"\"I#C2G6\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "%%*20*Cs2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+h/qOC !\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "f1:=h->(5775.+30030 *h)*2.^171960.-1;\n" }{MPLTEXT 1 0 18 "f2:=f1+2; f2(1);\n" }{MPLTEXT 1 0 28 "g:=h->1/ln(f1(h))/ln(f2(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 " f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"%vd\"\"!\"\"\",$*&\" &I+$F/F$F/F/F/F/)$\"\"#F.$\"'g> " 0 "" {MPLTEXT 1 0 35 "H:=2.^35; H/6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+PQ(fV$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+[-G " 0 "" {MPLTEXT 1 0 97 "C2*(1-1/3)^2/(1-2 /3)*(1-1/5)^2/(1-2/5)*(1-1/7)^2/(1-2/7)*(1-1/11)^2/(1-2/11)*(1-1/13)^2 /(1-2/13);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"&%Q;\"&65\"\"\"\"I# C2G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "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;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"$k$\"\"*\"\"\"I#C2G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "%*%%%; subs(C2=Cs2,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+qcbw(*!\")\"\"\"I#C2G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Z*3TX'!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# Cunningham chain I, length 3" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 34 "f1:=h->(3.+78*h)*2.^(273*128)-1;\n" }{MPLTEXT 1 0 32 "f2:=2*f1+1; f3:=2*f2+1; f3(1);\n" }{MPLTEXT 1 0 38 "g:=h->1/ln (f1(h))/ln(f2(h))/ln(f3(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"h G6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"\"$\"\"!\"\"\",$*&\"#yF/F$F/ F/F/F/)$\"\"#F.\"&W\\$F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ", &*&\"\"%\"\"\"I#f1G6\"F%F%\"\"$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +!y%GV]\"&70\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)oper atorGF%I&arrowGF%F%*(-I#lnG6$%*protectedGI(_syslibGF%6#-I#f1GF%F#!\"\" -F+6#-I#f2GF%F#F2-F+6#-I#f3GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^40; H/6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+G;^*4\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ $3P;r(!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "Cf1f2f3:=C3/(1 -1/2)^3/(1-1/3)^3*(1-1/13)^3/(1-3/13);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"&GL#\"$X)\"\"\"I#C3G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "%*%%; subs(C3=Cs3,%); HCCI3:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+2%f*G@!\"*\"\"\"I#C3G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+`OC_8!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5r,J \")\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# Cunningham ch ain I, length 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "f1:=h->( 375.+390*h)*2.^(77*128)-1;\n" }{MPLTEXT 1 0 44 "f2:=2*f1+1; f3:=2*f2+1 ; f4:=2*f3+1; f4(1);\n" }{MPLTEXT 1 0 48 "g:=h->1/ln(f1(h))/ln(f2(h))/ ln(f3(h))/ln(f4(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$ I)operatorGF%I&arrowGF%F%,&*&,&$\"$v$\"\"!\"\"\",$*&\"$!RF/F$F/F/F/F/) $\"\"#F.\"%c)*F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*& \"\"#\"\"\"I#f1G6\"F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"% \"\"\"I#f1G6\"F%F%\"\"$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\")\" \"\"I#f1G6\"F%F%\"\"(F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Av0va\"%h H" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arro wGF%F%**-I#lnG6$%*protectedGI(_syslibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f2GF% F#F2-F+6#-I#f3GF%F#F2-F+6#-I#f4GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^47; H/6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+%)[P29\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+dmRNj!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "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);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\")Koh5 \"'DYF\"\"\"I#C4G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "%*%%; subs(C4=Cs4,%); HCCI4:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$ *&$\"+9]A\\C!\"*\"\"\"I#C4G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+^ZCJv!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+T[ro=\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# Cunningham chain I, length 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "f1:=h->(255.+390*h)*2 .^(32*128)-1;\n" }{MPLTEXT 1 0 56 "f2:=2*f1+1; f3:=2*f2+1; f4:=2*f3+1; f5:=2*f4+1; f5(1);\n" }{MPLTEXT 1 0 58 "g:=h->1/ln(f1(h))/ln(f2(h))/l n(f3(h))/ln(f4(h))/ln(f5(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\" hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"$b#\"\"!\"\"\",$*&\"$!RF/F$ F/F/F/F/)$\"\"#F.\"%'4%F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ", &*&\"\"%\"\"\"I#f1G6\"F%F%\"\"$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&* &\"\")\"\"\"I#f1G6\"F%F%\"\"(F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*& \"#;\"\"\"I#f1G6\"F%F%\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+D$4y 2\"\"%G7" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF %I&arrowGF%F%*,-I#lnG6$%*protectedGI(_syslibGF%6#-I#f1GF%F#!\"\"-F+6#- I#f2GF%F#F2-F+6#-I#f3GF%F#F2-F+6#-I#f4GF%F#F2-F+6#-I#f5GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^54; H/6*(g(0)+4*g(H /2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+^)R9!=\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+qAZS\"*!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "Cf1f2f3f4f5:=C5*(1-1/2)/(1-1/2)^5*(1-2/3)/(1-1/3)^5* (1-4/5)/(1-1/5)^5*(1-2/7)/(1-4/7)*(1-1/13)^5/(1-5/13)*(1-7/17)/(1-5/17 );" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\")v= " 0 "" {MPLTEXT 1 0 33 "%*%%; subs(C5=Cs5,% ); HCCI5:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+YNam2S\"!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+G*QgG\"\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# Cunningham chain I, length 6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "f1:=h->(375.+390*h)*2.^(29*64)-1;\n " }{MPLTEXT 1 0 68 "f2:=2*f1+1; f3:=2*f2+1; f4:=2*f3+1; f5:=2*f4+1; f6 :=2*f4+1; f6(1);\n" }{MPLTEXT 1 0 68 "g:=h->1/ln(f1(h))/ln(f2(h))/ln(f 3(h))/ln(f4(h))/ln(f5(h))/ln(f6(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 " f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"$v$\"\"!\"\"\",$*&\" $!RF/F$F/F/F/F/)$\"\"#F.\"%c=F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"%\"\"\"I#f1G6\"F%F%\"\"$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\")\"\"\"I#f1G6\"F%F%\"\"(F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\"I#f1G6\"F%F%\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\"I#f1G6\"F%F%\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+@oj,j\"$`&" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG 6\"F%6$I)operatorGF%I&arrowGF%F%*.-I#lnG6$%*protectedGI(_syslibGF%6#-I #f1GF%F#!\"\"-F+6#-I#f2GF%F#F2-F+6#-I#f3GF%F#F2-F+6#-I#f4GF%F#F2-F+6#- I#f5GF%F#F2-F+6#-I#f6GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^60; H/6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+0:#H:\"\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ !4&p0@!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "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);" }} {PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"*]-'G8\"((>*>#\"\"\"I#C6G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "%*%%; subs(C6=Cs6,%); HC CI6:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+A^6s7!\")\"\"\"I#C6 G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+.6&RP#!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+)=^l&[\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# Cunningham chain I, length 6" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 81 "f1:=h->(375.+2*3*5*7*11*13*17*19*23*29*31*37*4 1*47*53*59*61*67*h)*2.^(29*64)-1;\n" }{MPLTEXT 1 0 68 "f2:=2*f1+1; f3: =2*f2+1; f4:=2*f3+1; f5:=2*f4+1; f6:=2*f4+1; f6(1);\n" }{MPLTEXT 1 0 68 "g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h))/ln(f6(h) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arr owGF%F%,&*&,&$\"$v$\"\"!\"\"\",$*&\"9IYwh3hyRm^F=F/F$F/F/F/F/)$\"\"#F. \"%c=F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\" \"I#f1G6\"F%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"%\"\"\"I#f 1G6\"F%F%\"\"$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\")\"\"\"I#f1G 6\"F%F%\"\"(F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\"I#f1G6\" F%F%\"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\"I#f1G6\"F%F% \"#:F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+EZS0:\"$u&" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%*.-I#lnG6$% *protectedGI(_syslibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f2GF%F#F2-F+6#-I#f3GF% F#F2-F+6#-I#f4GF%F#F2-F+6#-I#f5GF%F#F2-F+6#-I#f6GF%F#F2F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^60; H/6*(g(0)+4*g(H/2) +g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+0:#H:\"\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+S37%y\"!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "Cf1f2f3f4f5f6:=C6*(1-1/2)/(1-1/2)^6*(1-2/3)/(1-1/3)^ 6*(1-4/5)/(1-1/5)^6*(1-1/7)/(1-4/7)*(1-1/13)^6/(1-6/13)*(1-14/17)/(1-6 /17)*(1-5/31)/(1-6/31);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"*]-'G8 \"((>*>#\"\"\"I#C6G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "%*%%; subs(C6=Cs6,%); HCCI61:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+MA%y2\"!\")\"\"\"I#C6G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+](49,#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3x!>t&\"\")" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "# Cunnigham chain II, leng th 2 + twinprime" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f1:=h-> (5775.+30030*h)*2.^(1983*128)-1;\n" }{MPLTEXT 1 0 30 "f2:=f1+2; f3:=2* f2-1; f3(1);\n" }{MPLTEXT 1 0 28 "g:=h->1/ln(f1(h))/ln(f3(h));" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F %,&*&,&$\"%vd\"\"!\"\"\",$*&\"&I+$F/F$F/F/F/F/)$\"\"#F.\"'CQDF/F/F/!\" \"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I#f1G6\"\"\"\"\"\"#F%" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%\"\"$F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+#=-)3J\"&/k(" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%*&-I#lnG6$%*prot ectedGI(_syslibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f3GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^35; H/6*(g(0)+4*g(H/2)+g(H)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+PQ(fV$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+tok46!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "C2*(1-1/3)^2/(1-2/3)*(1-1/5)^2/(1-2/5)*(1-1/7)^2/(1-2/7)*(1-1/11)^ 2/(1-2/11)*(1-1/13)^2/(1-2/13);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&# \"&%Q;\"&65\"\"\"\"I#C2G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "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;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"$k$\"\"*\"\"\"I#C2G6 \"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "%*%%%; subs(C2=Cs 2,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+J^!z[%!\")\"\"\"I#C2G6 \"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+%pVF'H!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# Cunningham chain II, length 3" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f1:=h->(3.+6*h)*2.^(247*128 )+1;\n" }{MPLTEXT 1 0 32 "f2:=2*f1-1; f3:=2*f2-1; f3(1);\n" }{MPLTEXT 1 0 38 "g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"\"$\"\" !\"\"\",$*&\"\"'F/F$F/F/F/F/)$\"\"#F.\"&;;$F/F/F/F/F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"%\"\"\"I#f1G6\"F%F%\"\"$!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"++z+I$)\"%4&*" }}{PARA 11 "" 1 "" {XPPMATH 20 " f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%*(-I#lnG6$%*protectedGI(_sysl ibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f2GF%F#F2-F+6#-I#f3GF%F#F2F%F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^43; H/6*(g(0)+4*g(H/2) +g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+AI4'z)\"\"$" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+n/IF$)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Cf1f2f3:=C3*(1-1/2)/(1-1/2)^3*(1-2/3)/(1-1/3)^3;" }} {PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"\"*\"\"#\"\"\"I#C3G6\"F'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "%*%%; subs(C3=Cs3,%); HCCII3 :=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+5_GZP!\"*\"\"\"I#C3G6 \"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+e*\\,Q#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+`Xg&p$\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# Cunningham chain II, length 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f1:=h->(15.+30*h)*2.^(61*128)+1;\n" }{MPLTEXT 1 0 44 "f2:=2*f1-1; f3:=2*f2-1; f4:=2*f3-1; f4(1);\n" }{MPLTEXT 1 0 48 "g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"#:\" \"!\"\"\",$*&\"#IF/F$F/F/F/F/)$\"\"#F.\"%3yF/F/F/F/F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"%\"\"\"I#f1G6\"F%F%\"\"$!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 ",&*&\"\")\"\"\"I#f1G6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+w\">d'**\"%VB" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%**-I#lnG6$%*protectedGI(_sy slibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f2GF%F#F2-F+6#-I#f3GF%F#F2-F+6#-I#f4GF %F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^49; H/ 6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+M&*\\Hc\" \"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+2CB3k!#5" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 84 "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);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"%D6\"$G\"\"\"\"I#C4G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "%*%%; subs(C4=Cs4,%); HCCII4:=H/%;" }}{PARA 11 "" 1 " " {XPPMATH 20 ",$*&$\"+9bBKc!\"*\"\"\"I#C4G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+FV)=t\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+-b] ]K\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# Cunningham cha in II, length 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f1:=h->( 15.+30*h)*2.^(30*128)+1;\n" }{MPLTEXT 1 0 56 "f2:=2*f1-1; f3:=2*f2-1; \+ f4:=2*f3-1; f5:=2*f4-1; f5(1);\n" }{MPLTEXT 1 0 58 "g:=h->1/ln(f1(h))/ ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f5(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"#:\"\"!\"\"\",$* &\"#IF/F$F/F/F/F/)$\"\"#F.\"%SQF/F/F/F/F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\"I#f1G6\"F%F%F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"%\"\"\"I#f1G6\"F%F%\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\")\"\"\"I#f1G6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 ",&*&\"#;\"\"\"I#f1G6\"F%F%\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+hK0%\\'\"%\\6" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I \"hG6\"F%6$I)operatorGF%I&arrowGF%F%*,-I#lnG6$%*protectedGI(_syslibGF% 6#-I#f1GF%F#!\"\"-F+6#-I#f2GF%F#F2-F+6#-I#f3GF%F#F2-F+6#-I#f4GF%F#F2-F +6#-I#f5GF%F#F2F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H: =2.^54; H/6*(g(0)+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +^)R9!=\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+#yrFE\"!#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "Cf1f2f3f4f5:=C5*(1-1/2)/(1-1 /2)^5*(1-2/3)/(1-1/3)^5*(1-4/5)/(1-1/5)^5*(1-2/7)/(1-4/7);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"&vV)\"%[?\"\"\"I#C5G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "%*%%; subs(C5=Cs5,%); HCCII5:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+H%fC?&!\"*\"\"\"I#C5G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+l)eB8#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Y#3\"[%)\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# Cunningham chain II, length 6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f1:=h->(15.+30*h)*2.^(29*64)+1;\n" }{MPLTEXT 1 0 68 " f2:=2*f1-1; f3:=2*f2-1; f4:=2*f3-1; f5:=2*f4-1; f6:=2*f4-1; f6(1);\n" }{MPLTEXT 1 0 68 "g:=h->1/ln(f1(h))/ln(f2(h))/ln(f3(h))/ln(f4(h))/ln(f 5(h))/ln(f6(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)op eratorGF%I&arrowGF%F%,&*&,&$\"#:\"\"!\"\"\",$*&\"#IF/F$F/F/F/F/)$\"\"# F.\"%c=F/F/F/F/F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"#\"\"\" I#f1G6\"F%F%F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"%\"\"\"I# f1G6\"F%F%\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\")\"\"\"I #f1G6\"F%F%\"\"(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\"I #f1G6\"F%F%\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\"I# f1G6\"F%F%\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+*=Xoq$\"$_&" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF %F%*.-I#lnG6$%*protectedGI(_syslibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f2GF%F#F 2-F+6#-I#f3GF%F#F2-F+6#-I#f4GF%F#F2-F+6#-I#f5GF%F#F2-F+6#-I#f6GF%F#F2F %F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "H:=2.^58; H/6*(g(0 )+4*g(H/2)+g(H));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iPI#)G\"\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+_xtb`!#6" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 106 "Cf1f2f3f4f5f6:=C6*(1-1/2)/(1-1/2)^6*(1-2/3)/(1-1/3 )^6*(1-4/5)/(1-1/5)^6*(1-1/7)/(1-4/7)*(1-5/31)/(1-6/31);" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&#\"'v[R\"%[?\"\"\"I#C6G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "%*%%; subs(C6=Cs6,%); HCCII6:=H/%;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+5,kK5!\")\"\"\"I#C6G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Rg0F>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+PJq&\\\"\"\")" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "1.9. K" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "rd" }{TEXT 206 8 "\30 3\251" }{TEXT 206 2 "s." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 16 "1.10 . Eratoszten" }{TEXT 206 8 "\303\251" }{TEXT 206 7 "sz szit" }{TEXT 206 8 "\303\241" }{TEXT 206 3 "ja." }}{PARA 0 "" 0 "" {TEXT 201 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "sieve:=proc(N::posint) loca l n,B,i,j;\n" }{MPLTEXT 1 0 20 "n:=floor((N-1)/2);\n" }{MPLTEXT 1 0 19 "B:=Array(0..n-1);\n" }{MPLTEXT 1 0 36 "for j from 0 to n-1 do B[j] :=1 od;\n" }{MPLTEXT 1 0 7 "j:=0;\n" }{MPLTEXT 1 0 14 "while j=n then break fi;\n" } {MPLTEXT 1 0 40 " while iF*-I&floorGF&6#,&*&#\"\"\"\"\"#F6F%F6F6F5!\"\">F+-I&Arr ayGF(6#;\"\"!,&F*F6F6F8?(F-F>F6F?I%trueGF(>&F+6#F-F6>F-F>?(F&F6F6F&2F- F*C'?(F&F6F6F&/FCF>>F-,&F-F6F6F6>F,,(*&F7F6)F-F7F6F6*&\"\"'F6F-F6F6\" \"$F6@$1F*F,[?(F&F6F6F&2F,F*C$>&F+6#F,F>>F,,(F,F6*&F7F6F-F6F6FSF6FKF+F &F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "debug(sieve); siev e(21);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&sieveG6\"" }}{PARA 9 "" 1 "" {TEXT 207 28 "\{--> enter sieve, args = 21" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&ArrayG%*protecte dG6#/I$%idG6\"\"*g(f8:" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&ArrayG%*protectedG6#/I$%idG6\"\"*g(f8:" }} {PARA 9 "" 1 "" {TEXT 207 134 "<-- exit sieve (now at top level) = Arr ay(0..9, \{(1) = 1, (2) = 1, (3) = 1, (4) = 0, (5) = 1, (6) = 1, (7) = 0, (8) = 1, (9) = 1\})\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&ArrayG%* protectedG6#/I$%idG6\"\"*g(f8:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "undebug(sieve); sieve(10000);" }}{PARA 11 "" 1 "" {XPPMATH 20