{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%$\"% " 0 "" {MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 57 "# This procedure appr oximate Cs calculating the product\n" }{MPLTEXT 1 0 23 "# for primes b elow x.\n" }{MPLTEXT 1 0 3 "#\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 42 "Cs:=proc(s::posint,x::posint) local P,p;\n" }{MPLTEXT 1 0 25 "P:=1 .; p:=nextprime(s);\n" }{MPLTEXT 1 0 58 "while pF,$\"\"\"\"\"!>F--I*nextprimeG6$F(I(_syslibGF&6#F%?(F&F 1F1F&2F-F*C$>F,*(F,F1,&F1F1*&F%F1F-!\"\"F@F1),&F1F1*$F-F@F@F%F@>F--F56 #F-F,F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "Cs(2,10); Cs (2,100); Cs(2,1000); Cs(2,10000); Cs(2,100000); Cs(2,1000000);" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+)\\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$=;g'! #5" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 6 "1.8. P" }{TEXT 206 8 "\30 3\251" }{TEXT 206 4 "lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f1:=h->(3.+30*h)*2.^38880.-1;\n" } {MPLTEXT 1 0 18 "f2:=f1+2; f2(0);\n" }{MPLTEXT 1 0 28 "g:=h->1/ln(f1(h ))/ln(f2(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)opera torGF%I&arrowGF%F%,&*&,&$\"\"$\"\"!\"\"\",$*&\"#IF/F$F/F/F/F/)$\"\"#F. $\"&!))QF.F/F/F/!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I#f1G6 \"\"\"\"\"\"#F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+GG(pL$\"&&p6" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F %*&-I#lnG6$%*protectedGI(_syslibGF%6#-I#f1GF%F#!\"\"-F+6#-I#f2GF%F#F2F %F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "2.^27/6*(g(0)+4*g( 2.^26)+g(2.^27));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fE`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 ",$*&\"#?\"\"\"I#C2G6\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "%%*20*0.66016;" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+! o$pOC!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "f1:=h->(5775.+ 30030*h)*2.^171960.-1;\n" }{MPLTEXT 1 0 18 "f2:=f1+2; f2(0);\n" } {MPLTEXT 1 0 28 "g:=h->1/ln(f1(h))/ln(f2(h));" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"hG6\"F%6$I)operatorGF%I&arrowGF%F%,&*&,&$\"%vd\"\" !\"\"\",$*&\"&I+$F/F$F/F/F/F/)$\"\"#F.$\"'g> " 0 " " {MPLTEXT 1 0 35 "2.^33/6*(g(0)+4*g(2.^32)+g(2.^33));" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+CxJVg!#5" }}}{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 ", $*&#\"&%Q;\"&65\"\"\"\"I#C2G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Cf1f2:=%/(1-1/2)^2/(1-1/3)^2/(1-1/5)^2/(1-1/7)^2/(1-1 /11)^2/(1-1/13)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"$k$\"\"*\" \"\"I#C2G6\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "%*%%%; \+ subs(C2=0.66016,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&$\"+zi=WC!\") \"\"\"I#C2G6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+9Sb8;!\")" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT 206 6 "1.9. K" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "rd" }{TEXT 206 8 "\303\251" }{TEXT 206 2 "s." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 16 "1.10. Eratoszten" }{TEXT 206 8 "\303\25 1" }{TEXT 206 7 "sz szit" }{TEXT 206 8 "\303\241" }{TEXT 206 3 "ja." } }{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "sieve:=proc(N::posint) local n,B,i,j;\n" }{MPLTEXT 1 0 20 "n:=fl oor((N-1)/2);\n" }{MPLTEXT 1 0 19 "B:=Array(0..n-1);\n" }{MPLTEXT 1 0 36 "for j from 0 to n-1 do B[j]:=1 od;\n" }{MPLTEXT 1 0 7 "j:=0;\n" } {MPLTEXT 1 0 14 "while j=n then break fi;\n" }{MPLTEXT 1 0 40 " while iF*-I&floorGF&6#,&*&#\"\"\" \"\"#F6F%F6F6F5!\"\">F+-I&ArrayGF(6#;\"\"!,&F*F6F6F8?(F-F>F6F?I%trueGF (>&F+6#F-F6>F-F>?(F&F6F6F&2F-F*C'?(F&F6F6F&/FCF>>F-,&F-F6F6F6>F,,(*&F7 F6)F-F7F6F6*&\"\"'F6F-F6F6\"\"$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); sieve(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%*protectedG6#/I$%idG6\"\"*GMXc\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{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%*protecte dG6#/I$%idG6\"\"*GMXc\"" }}{PARA 9 "" 1 "" {TEXT 207 134 "<-- exit sie ve (now at top level) = Array(0..9, \{(1) = 1, (2) = 1, (3) = 1, (4) = 0, (5) = 1, (6) = 1, (7) = 0, (8) = 1, (9) = 1\})\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&ArrayG%*protectedG6#/I$%idG6\"\"*GMXc\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "undebug(sieve); sieve(10000);" }} {PARA 11 "" 1 "" {XPPMATH 20 "I&sieveG6\"" }}{PARA 11 "" 1 ""