Carmichael 3 strong pseudoprimes: Difference between revisions

← Older edit

Carmichael 3 strong pseudoprimes (view source)

Revision as of 09:19, 13 November 2023

10,009 bytes added , 6 months ago

m

→‎{{header|RPL}}: tweaked the code

Aerobar

1,150

edits

Revision as of 19:02, 26 August 2022 (view source) Thundergnat (talk \| contribs) m (syntax highlighting fixup automation) ← Older edit		Latest revision as of 09:19, 13 November 2023 (view source) Aerobar (talk \| contribs) m (→‎{{header\|RPL}}: tweaked the code)
(9 intermediate revisions by 8 users not shown)
Line 33: [[Chernick's Carmichael numbers]] <br><br> =={{header\|11l}}== {{trans\|D}} <syntaxhighlight lang="11l">F mod_(n, m) R ((n % m) + m) % m Line 88 ⟶ 87: 61 x 3361 x 4021 </pre> =={{header\|Ada}}== Uses the Miller_Rabin package from [[Miller-Rabin primality test#ordinary integers]]. <syntaxhighlight lang=~~Ada~~"ada">with Ada.Text_IO, Miller_Rabin; procedure Nemesis is Line 147 ⟶ 145: 61 * 241 * 421 = 6189121 61 * 3361 * 4021 = 824389441</pre> =={{header\|ALGOL 68}}== Uses the Sieve of Eratosthenes code from the Smith Numbers task with an increased upper-bound (included here for convenience). <syntaxhighlight lang="algol68"># sieve of Eratosthene: sets s[i] to TRUE if i is prime, FALSE otherwise # PROC sieve = ( REF[]BOOL s )VOID: BEGIN Line 182 ⟶ 179: IF is prime[ prime3 ] THEN IF ( prime2 * prime3 ) MOD ( prime1 - 1 ) = 1 THEN print( ( whole( prime1, 0 ), " ", whole( prime2, 0 ), " ", whole( prime3, 0 )~~, newline~~ ) ); print( ( newline ) ) FI FI Line 221 ⟶ 219: 61 3361 4021 </pre> =={{header\|Arturo}}== <syntaxhighlight lang="arturo">printOneLine: function [a,b,c,d]-> print [ pad to :string a 3 "x" pad to :string b 5 "x" pad to :string c 5 "=" pad to :string d 10 ] 2..61 \| select => prime? \| loop 'p -> loop 2..p 'h3 [ g: h3 + p loop 1..g 'd -> if and? -> zero? mod gp-1 d -> zero? mod d+pp h3 [ q: 1 + ((p-1)g)/d if prime? q [ r: 1 + (p q) / h3 if and? [prime? r] [one? (qr) % p-1]-> printOneLine p q r (pqr) ] ] ]</syntaxhighlight> {{out}} <pre> 3 x 11 x 17 = 561 3 x 3 x 5 = 45 5 x 29 x 73 = 10585 5 x 5 x 13 = 325 5 x 17 x 29 = 2465 5 x 13 x 17 = 1105 7 x 19 x 67 = 8911 7 x 31 x 73 = 15841 7 x 13 x 31 = 2821 7 x 23 x 41 = 6601 7 x 7 x 13 = 637 7 x 73 x 103 = 52633 7 x 13 x 19 = 1729 11 x 11 x 61 = 7381 11 x 11 x 41 = 4961 11 x 11 x 31 = 3751 13 x 61 x 397 = 314821 13 x 37 x 241 = 115921 13 x 97 x 421 = 530881 13 x 37 x 97 = 46657 13 x 37 x 61 = 29341 17 x 41 x 233 = 162401 17 x 17 x 97 = 28033 17 x 353 x 1201 = 7207201 19 x 43 x 409 = 334153 19 x 19 x 181 = 65341 19 x 19 x 73 = 26353 19 x 19 x 37 = 13357 19 x 199 x 271 = 1024651 23 x 23 x 89 = 47081 23 x 23 x 67 = 35443 23 x 199 x 353 = 1615681 29 x 29 x 421 = 354061 29 x 113 x 1093 = 3581761 29 x 29 x 281 = 236321 29 x 197 x 953 = 5444489 31 x 991 x 15361 = 471905281 31 x 61 x 631 = 1193221 31 x 151 x 1171 = 5481451 31 x 31 x 241 = 231601 31 x 61 x 271 = 512461 31 x 61 x 211 = 399001 31 x 271 x 601 = 5049001 31 x 31 x 61 = 58621 31 x 181 x 331 = 1857241 37 x 109 x 2017 = 8134561 37 x 73 x 541 = 1461241 37 x 613 x 1621 = 36765901 37 x 73 x 181 = 488881 37 x 37 x 73 = 99937 37 x 73 x 109 = 294409 41 x 1721 x 35281 = 2489462641 41 x 881 x 12041 = 434932961 41 x 41 x 281 = 472361 41 x 41 x 241 = 405121 41 x 101 x 461 = 1909001 41 x 241 x 761 = 7519441 41 x 241 x 521 = 5148001 41 x 73 x 137 = 410041 41 x 61 x 101 = 252601 43 x 631 x 13567 = 368113411 43 x 271 x 5827 = 67902031 43 x 127 x 2731 = 14913991 43 x 43 x 463 = 856087 43 x 127 x 1093 = 5968873 43 x 211 x 757 = 6868261 43 x 631 x 1597 = 43331401 43 x 127 x 211 = 1152271 43 x 211 x 337 = 3057601 43 x 433 x 643 = 11972017 43 x 547 x 673 = 15829633 43 x 3361 x 3907 = 564651361 47 x 47 x 277 = 611893 47 x 47 x 139 = 307051 47 x 3359 x 6073 = 958762729 47 x 1151 x 1933 = 104569501 47 x 3727 x 5153 = 902645857 53 x 53 x 937 = 2632033 53 x 157 x 2081 = 17316001 53 x 79 x 599 = 2508013 53 x 53 x 313 = 879217 53 x 157 x 521 = 4335241 53 x 53 x 157 = 441013 59 x 59 x 1741 = 6060421 59 x 59 x 349 = 1214869 59 x 59 x 233 = 811073 59 x 1451 x 2089 = 178837201 61 x 421 x 12841 = 329769721 61 x 181 x 5521 = 60957361 61 x 61 x 1861 = 6924781 61 x 1301 x 19841 = 1574601601 61 x 277 x 2113 = 35703361 61 x 181 x 1381 = 15247621 61 x 541 x 3001 = 99036001 61 x 661 x 2521 = 101649241 61 x 271 x 571 = 9439201 61 x 241 x 421 = 6189121 61 x 3361 x 4021 = 824389441</pre> =={{header\|AWK}}== <syntaxhighlight lang=~~AWK~~"awk"> # syntax: GAWK -f CARMICHAEL_3_STRONG_PSEUDOPRIMES.AWK # converted from C Line 342 ⟶ 470: </pre> =={{header\|BASIC}}== ==={{header\|BASIC256}}=== {{trans\|FreeBASIC}} <syntaxhighlight lang=~~BASIC256~~"vbnet">for i = 3 to max_sieve step 2 ~~for i = 3 to max_sieve step 2~~ isprime[i] = 1 next i Line 380 ⟶ 507: for i = 2 to 61 call carmichael3(i) next i end</syntaxhighlight> ==={{header\|Chipmunk Basic}}=== {{trans\|FreeBASIC}} {{works with\|Chipmunk Basic\|3.6.4}} <syntaxhighlight lang="vbnet">100 cls 110 max_sieve = 10000000 ' 10^7 120 dim isprime(max_sieve) 130 sub carmichael3(p1) 140 if isprime(p1) = 0 then goto 440 150 for h3 = 1 to p1-1 160 t1 = (h3+p1)(p1-1) 170 t2 = (-p1p1) mod h3 180 if t2 < 0 then t2 = t2+h3 190 for d = 1 to h3+p1-1 200 if t1 mod d = 0 and t2 = (d mod h3) then 210 p2 = 1+int(t1/d) 220 if isprime(p2) = 0 then goto 270 230 p3 = 1+int(p1p2/h3) 240 if isprime(p3) = 0 or ((p2p3) mod (p1-1)) <> 1 then goto 270 250 print format$(p1,"###");" ";format$(p2,"####");" * ";format$(p3,"#####") 260 endif 270 next d 280 next h3 290 end sub 300 'set up sieve 310 for i = 3 to max_sieve step 2 320 isprime(i) = 1 330 next i 340 isprime(2) = 1 350 for i = 3 to sqr(max_sieve) step 2 360 if isprime(i) = 1 then 370 for j = ii to max_sieve step i2 380 isprime(j) = 0 390 next j 400 endif 410 next i 420 for i = 2 to 61 430 carmichael3(i) 440 next i 450 end</syntaxhighlight> ==={{header\|FreeBASIC}}=== <syntaxhighlight lang="freebasic">' version 17-10-2016 ' compile with: fbc -s console ' using a sieve for finding primes #Define max_sieve 10000000 ' 10^7 ReDim Shared As Byte isprime(max_sieve) ' translated the pseudo code to FreeBASIC Sub carmichael3(p1 As Integer) If isprime(p1) = 0 Then Exit Sub Dim As Integer h3, d, p2, p3, t1, t2 For h3 = 1 To p1 -1 t1 = (h3 + p1) * (p1 -1) t2 = (-p1 * p1) Mod h3 If t2 < 0 Then t2 = t2 + h3 For d = 1 To h3 + p1 -1 If t1 Mod d = 0 And t2 = (d Mod h3) Then p2 = 1 + (t1 \ d) If isprime(p2) = 0 Then Continue For p3 = 1 + (p1 * p2 \ h3) If isprime(p3) = 0 Or ((p2 * p3) Mod (p1 -1)) <> 1 Then Continue For Print Using "### * #### * #####"; p1; p2; p3 End If Next d Next h3 End Sub ' ------=< MAIN >=------ Dim As UInteger i, j 'set up sieve For i = 3 To max_sieve Step 2 isprime(i) = 1 Next i isprime(2) = 1 For i = 3 To Sqr(max_sieve) Step 2 If isprime(i) = 1 Then For j = i * i To max_sieve Step i * 2 isprime(j) = 0 Next j End If Next i For i = 2 To 61 carmichael3(i) Next i ' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</syntaxhighlight> {{out}} <pre> 3 * 11 * 17 5 * 29 * 73 5 * 17 * 29 5 * 13 * 17 7 * 19 * 67 7 * 31 * 73 7 * 13 * 31 7 * 23 * 41 7 * 73 * 103 7 * 13 * 19 13 * 61 * 397 13 * 37 * 241 13 * 97 * 421 13 * 37 * 97 13 * 37 * 61 17 * 41 * 233 17 * 353 * 1201 19 * 43 * 409 19 * 199 * 271 23 * 199 * 353 29 * 113 * 1093 29 * 197 * 953 31 * 991 * 15361 31 * 61 * 631 31 * 151 * 1171 31 * 61 * 271 31 * 61 * 211 31 * 271 * 601 31 * 181 * 331 37 * 109 * 2017 37 * 73 * 541 37 * 613 * 1621 37 * 73 * 181 37 * 73 * 109 41 * 1721 * 35281 41 * 881 * 12041 41 * 101 * 461 41 * 241 * 761 41 * 241 * 521 41 * 73 * 137 41 * 61 * 101 43 * 631 * 13567 43 * 271 * 5827 43 * 127 * 2731 43 * 127 * 1093 43 * 211 * 757 43 * 631 * 1597 43 * 127 * 211 43 * 211 * 337 43 * 433 * 643 43 * 547 * 673 43 * 3361 * 3907 47 * 3359 * 6073 47 * 1151 * 1933 47 * 3727 * 5153 53 * 157 * 2081 53 * 79 * 599 53 * 157 * 521 59 * 1451 * 2089 61 * 421 * 12841 61 * 181 * 5521 61 * 1301 * 19841 61 * 277 * 2113 61 * 181 * 1381 61 * 541 * 3001 61 * 661 * 2521 61 * 271 * 571 61 * 241 * 421 61 * 3361 * 4021</pre> ==={{header\|Gambas}}=== {{trans\|FreeBASIC}} <syntaxhighlight lang="vbnet">Public isprime[1000000] As Integer Public Sub Main() Dim max_sieve As Integer = 1000000 Dim i As Integer, j As Integer 'set up sieve For i = 3 To max_sieve Step 2 isprime[i] = 1 Next isprime[2] = 1 For i = 3 To Sqr(max_sieve) Step 2 If isprime[i] = 1 Then For j = i * i To max_sieve Step i * 2 isprime[j] = 0 Next End If Next For i = 2 To 61 If isprime[i] <> 0 Then carmichael3(i) Next End Sub carmichael3(p1 As Integer) Dim h3 As Integer, d As Integer Dim p2 As Integer, p3 As Integer, t1 As Integer, t2 As Integer For h3 = 1 To p1 - 1 t1 = (h3 + p1) * (p1 - 1) t2 = (-p1 * p1) Mod h3 If t2 < 0 Then t2 = t2 + h3 For d = 1 To h3 + p1 - 1 If t1 Mod d = 0 And t2 = (d Mod h3) Then p2 = 1 + (t1 \ d) If isprime[p2] = 0 Then Continue p3 = 1 + ((p1 * p2) \ h3) If isprime[p3] = 0 Or ((p2 * p3) Mod (p1 - 1)) <> 1 Then Continue Print Format$(p1, "###"); " * "; Format$(p2, "####"); " * "; Format$(p3, "#####") End If Next Next End Sub</syntaxhighlight> ==={{header\|Yabasic}}=== {{trans\|FreeBASIC}} <syntaxhighlight lang="vbnet">max_sieve = 1e7 dim isprime(max_sieve) //set up sieve for i = 3 to max_sieve step 2 isprime(i) = 1 next i isprime(2) = 1 for i = 3 to sqrt(max_sieve) step 2 if isprime(i) = 1 then for j = i * i to max_sieve step i * 2 isprime(j) = 0 next j fi next i for i = 2 to 61 carmichael3(i) next i end ~~</syntaxhighlight>~~ sub carmichael3(p1) local h3, d, p2, p3, t1, t2 if isprime(p1) = 0 return for h3 = 1 to p1 -1 t1 = (h3 + p1) * (p1 -1) t2 = mod((-p1 * p1), h3) if t2 < 0 t2 = t2 + h3 for d = 1 to h3 + p1 -1 if mod(t1, d) = 0 and t2 = mod(d, h3) then p2 = 1 + int(t1 / d) if isprime(p2) = 0 continue p3 = 1 + int(p1 * p2 / h3) if isprime(p3) = 0 or mod((p2 * p3), (p1 -1)) <> 1 continue print p1 using ("###"), " * ", p2 using ("####"), " * ", p3 using ("#####") fi next d next h3 end sub</syntaxhighlight> ==={{header\|ZX Spectrum Basic}}=== {{trans\|C}} <syntaxhighlight lang="zxbasic">10 FOR p=2 TO 61 20 LET n=p: GO SUB 1000 30 IF NOT n THEN GO TO 200 40 FOR h=1 TO p-1 50 FOR d=1 TO h-1+p 60 IF NOT (FN m((h+p)(p-1),d)=0 AND FN w(-pp,h)=FN m(d,h)) THEN GO TO 180 70 LET q=INT (1+((p-1)(h+p)/d)) 80 LET n=q: GO SUB 1000 90 IF NOT n THEN GO TO 180 100 LET r=INT (1+(pq/h)) 110 LET n=r: GO SUB 1000 120 IF (NOT n) OR ((FN m((qr),(p-1))<>1)) THEN GO TO 180 130 PRINT p;" ";q;" ";r 180 NEXT d 190 NEXT h 200 NEXT p 210 STOP 1000 IF n<4 THEN LET n=(n>1): RETURN 1010 IF (NOT FN m(n,2)) OR (NOT FN m(n,3)) THEN LET n=0: RETURN 1020 LET i=5 1030 IF NOT ((ii)<=n) THEN LET n=1: RETURN 1040 IF (NOT FN m(n,i)) OR NOT FN m(n,(i+2)) THEN LET n=0: RETURN 1050 LET i=i+6 1060 GO TO 1030 2000 DEF FN m(a,b)=a-(INT (a/b)b): REM Mod function 2010 DEF FN w(a,b)=FN m(FN m(a,b)+b,b): REM Mod function modified </syntaxhighlight> =={{header\|C}}== <syntaxhighlight lang=C"c"> #include <stdio.h> Line 454 ⟶ 874: 61 3361 4021 </pre> =={{header\|C++}}== <syntaxhighlight lang="cpp">#include <iomanip> #include <iostream> Line 583 ⟶ 1,002: 61 x 3361 x 4021 = 824389441 </pre> =={{header\|Clojure}}== <syntaxhighlight lang="lisp"> (ns example (:gen-class)) Line 688 ⟶ 1,106: </pre> =={{header\|D}}== <syntaxhighlight lang="d">enum mod = (in int n, in int m) pure nothrow @nogc=> ((n % m) + m) % m; bool isPrime(in uint n) pure nothrow @nogc { Line 793 ⟶ 1,210: 61 x 241 x 421 61 x 3361 x 4021</pre> =={{header\|EasyLang}}== {{trans\|C}} <syntaxhighlight> func isprim num . i = 2 while i <= sqrt num if num mod i = 0 return 0 . i += 1 . return 1 . proc carmichael3 p1 . . for h3 = 1 to p1 - 1 for d = 1 to h3 + p1 - 1 if (h3 + p1) (p1 - 1) mod d = 0 and -p1 * p1 mod h3 = d mod h3 p2 = 1 + (p1 - 1) * (h3 + p1) div d if isprim p2 = 1 p3 = 1 + (p1 * p2 div h3) if isprim p3 = 1 and (p2 * p3) mod (p1 - 1) = 1 print p1 & " " & p2 & " " & p3 . . . . . . for p1 = 2 to 61 if isprim p1 = 1 carmichael3 p1 . . </syntaxhighlight> =={{header\|EchoLisp}}== <syntaxhighlight lang="scheme"> ;; charmichaël numbers up to N-th prime ; 61 is 18-th prime (define (charms (N 18) local: (h31 0) (Prime2 0) (Prime3 0)) Line 812 ⟶ 1,263: </syntaxhighlight> {{out}} <syntaxhighlight lang="scheme"> (charms 3) 💥 561 = 3 x 11 x 17 Line 839 ⟶ 1,290: =={{header\|F_Sharp\|F#}}== This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_function Extensible Prime Generator (F#)] <syntaxhighlight lang="fsharp"> // Carmichael Number . Nigel Galloway: November 19th., 2017 let fN n = Seq.collect ((fun g->(Seq.map(fun e->(n,1+(n-1)(n+g)/e,g,e))){1..(n+g-1)})){2..(n-1)} Line 921 ⟶ 1,372: 61 x 3361 x 4021 = 824389441 </pre> =={{header\|Factor}}== Note the use of <code>rem</code> instead of <code>mod</code> when the remainder should always be positive. <syntaxhighlight lang="factor">USING: formatting kernel locals math math.primes math.ranges sequences ; IN: rosetta-code.carmichael Line 1,019 ⟶ 1,469: 61 3361 4021 </pre> =={{header\|Fortran}}== ===Plan=== This is F77 style, and directly translates the given calculation as per ''formula translation''. It turns out that the normal integers suffice for the demonstration, except for just one of the products of the three primes: 41x1721x35281 = 2489462641, which is bigger than 2147483647, the 32-bit limit. Fortunately, INTEGER8 variables are also available, so the extension is easy. Otherwise, one would have to mess about with using two integers in a bignum style, one holding say the millions, and the second the number up to a million. ===Source=== So, using the double MOD approach (see the ''Discussion'') - which gives the same result for either style of MOD... <syntaxhighlight lang=~~Fortran~~"fortran"> LOGICAL FUNCTION ISPRIME(N) !Ad-hoc, since N is not going to be big... INTEGER N !Despite this intimidating allowance of 32 bits... INTEGER F !A possible factor. Line 1,139 ⟶ 1,588: 61 3361 4021 824389441 </pre> ~~=={{header\|FreeBASIC}}==~~ ~~<syntaxhighlight lang=freebasic>' version 17-10-2016~~ ~~' compile with: fbc -s console~~ ~~' using a sieve for finding primes~~ ~~#Define max_sieve 10000000 ' 10^7~~ ~~ReDim Shared As Byte isprime(max_sieve)~~ ~~' translated the pseudo code to FreeBASIC~~ ~~Sub carmichael3(p1 As Integer)~~ ~~If isprime(p1) = 0 Then Exit Sub~~ ~~Dim As Integer h3, d, p2, p3, t1, t2~~ ~~For h3 = 1 To p1 -1~~ ~~t1 = (h3 + p1) * (p1 -1)~~ ~~t2 = (-p1 * p1) Mod h3~~ ~~If t2 < 0 Then t2 = t2 + h3~~ ~~For d = 1 To h3 + p1 -1~~ ~~If t1 Mod d = 0 And t2 = (d Mod h3) Then~~ ~~p2 = 1 + (t1 \ d)~~ ~~If isprime(p2) = 0 Then Continue For~~ ~~p3 = 1 + (p1 * p2 \ h3)~~ ~~If isprime(p3) = 0 Or ((p2 * p3) Mod (p1 -1)) <> 1 Then Continue For~~ ~~Print Using "### * #### * #####"; p1; p2; p3~~ ~~End If~~ ~~Next d~~ ~~Next h3~~ ~~End Sub~~ ~~' ------=< MAIN >=------~~ ~~Dim As UInteger i, j~~ ~~'set up sieve~~ ~~For i = 3 To max_sieve Step 2~~ ~~isprime(i) = 1~~ ~~Next i~~ ~~isprime(2) = 1~~ ~~For i = 3 To Sqr(max_sieve) Step 2~~ ~~If isprime(i) = 1 Then~~ ~~For j = i * i To max_sieve Step i * 2~~ ~~isprime(j) = 0~~ ~~Next j~~ ~~End If~~ ~~Next i~~ ~~For i = 2 To 61~~ ~~carmichael3(i)~~ ~~Next i~~ ~~' empty keyboard buffer~~ ~~While InKey <> "" : Wend~~ ~~Print : Print "hit any key to end program"~~ ~~Sleep~~ ~~End</syntaxhighlight>~~ ~~{{out}}~~ ~~<pre> 3 * 11 * 17~~ ~~5 * 29 * 73~~ ~~5 * 17 * 29~~ ~~5 * 13 * 17~~ ~~7 * 19 * 67~~ ~~7 * 31 * 73~~ ~~7 * 13 * 31~~ ~~7 * 23 * 41~~ ~~7 * 73 * 103~~ ~~7 * 13 * 19~~ ~~13 * 61 * 397~~ ~~13 * 37 * 241~~ ~~13 * 97 * 421~~ ~~13 * 37 * 97~~ ~~13 * 37 * 61~~ ~~17 * 41 * 233~~ ~~17 * 353 * 1201~~ ~~19 * 43 * 409~~ ~~19 * 199 * 271~~ ~~23 * 199 * 353~~ ~~29 * 113 * 1093~~ ~~29 * 197 * 953~~ ~~31 * 991 * 15361~~ ~~31 * 61 * 631~~ ~~31 * 151 * 1171~~ ~~31 * 61 * 271~~ ~~31 * 61 * 211~~ ~~31 * 271 * 601~~ ~~31 * 181 * 331~~ ~~37 * 109 * 2017~~ ~~37 * 73 * 541~~ ~~37 * 613 * 1621~~ ~~37 * 73 * 181~~ ~~37 * 73 * 109~~ ~~41 * 1721 * 35281~~ ~~41 * 881 * 12041~~ ~~41 * 101 * 461~~ ~~41 * 241 * 761~~ ~~41 * 241 * 521~~ ~~41 * 73 * 137~~ ~~41 * 61 * 101~~ ~~43 * 631 * 13567~~ ~~43 * 271 * 5827~~ ~~43 * 127 * 2731~~ ~~43 * 127 * 1093~~ ~~43 * 211 * 757~~ ~~43 * 631 * 1597~~ ~~43 * 127 * 211~~ ~~43 * 211 * 337~~ ~~43 * 433 * 643~~ ~~43 * 547 * 673~~ ~~43 * 3361 * 3907~~ ~~47 * 3359 * 6073~~ ~~47 * 1151 * 1933~~ ~~47 * 3727 * 5153~~ ~~53 * 157 * 2081~~ ~~53 * 79 * 599~~ ~~53 * 157 * 521~~ ~~59 * 1451 * 2089~~ ~~61 * 421 * 12841~~ ~~61 * 181 * 5521~~ ~~61 * 1301 * 19841~~ ~~61 * 277 * 2113~~ ~~61 * 181 * 1381~~ ~~61 * 541 * 3001~~ ~~61 * 661 * 2521~~ ~~61 * 271 * 571~~ ~~61 * 241 * 421~~ ~~61 * 3361 * 4021</pre>~~ =={{header\|Go}}== <syntaxhighlight lang="go">package main import "fmt" Line 1,397 ⟶ 1,715: 61 3361 4021 824389441 </pre> =={{header\|Haskell}}== {{trans\|Ruby}} Line 1,403 ⟶ 1,720: {{Works with\|GHC\|7.4.1}} {{Works with\|primes\|0.2.1.0}} <syntaxhighlight lang="haskell">#!/usr/bin/runhaskell import Data.Numbers.Primes Line 1,493 ⟶ 1,810: (61,3361,4021) </pre> =={{header\|Icon}} and {{header\|Unicon}}== The following works in both languages. <syntaxhighlight lang="unicon">link "factors" procedure main(A) Line 1,554 ⟶ 1,870: -> </pre> =={{header\|J}}== <syntaxhighlight lang=J"j"> q =: (,"0 1~ >:@i.@<:@+/"1)&.>@(,&.>"0 1~ >:@i.)&.>@I.@(1&p:@i.)@>: f1 =: (0: = {. \| <:@{: * 1&{ + {:) . ((1&{ \| -@:@{:) = 1&{ \| {.) Line 1,636 ⟶ 1,951: 61 3361 4021 </pre> =={{header\|Java}}== {{trans\|D}} <syntaxhighlight lang="java">public class Test { static int mod(int n, int m) { Line 1,747 ⟶ 2,061: 61 x 241 x 421 61 x 3361 x 4021</pre> =={{header\|Julia}}== This solution is a straightforward implementation of the algorithm of the Jameson paper cited in the task description. Just for fun, I use Julia's capacity to accommodate Unicode identifiers to match some of the paper's symbols to the variables used in the <tt>carmichael</tt> function. '''Function''' <syntaxhighlight lang="julia">using Primes function carmichael(pmax::Integer) Line 1,775 ⟶ 2,088: '''Main''' <syntaxhighlight lang="julia">hi = 61 car = carmichael(hi) Line 1,843 ⟶ 2,156: 42 results in total.</pre> =={{header\|Kotlin}}== {{trans\|D}} <syntaxhighlight lang="scala">fun Int.isPrime(): Boolean { return when { this == 2 -> true Line 1,884 ⟶ 2,196: {{out}} See D output. =={{header\|Lua}}== <syntaxhighlight lang="lua">local function isprime(n) if n < 2 then return false end if n % 2 == 0 then return n==2 end Line 1,998 ⟶ 2,309: 61 × 3361 × 4021 = 824389441 69 found.</pre> =={{header\|Mathematica}} / {{header\|Wolfram Language}}== <syntaxhighlight lang="mathematica">Cases[Cases[ Cases[Table[{p1, h3, d}, {p1, Array[Prime, PrimePi@61]}, {h3, 2, p1 - 1}, {d, 1, h3 + p1 - 1}], {p1_Integer, h3_, d_} /; Line 2,008 ⟶ 2,318: p2, 1 + Floor[p1 p2/h3]}], {p1_, p2_, p3_} /; Mod[p2 p3, p1 - 1] == 1 :> Print[p1, "", p2, "", p3]]</syntaxhighlight> =={{header\|Nim}}== {{trans\|Vala}} with some modifications <syntaxhighlight lang="nim">import strformat func isPrime(n: int64): bool = Line 2,114 ⟶ 2,423: 61 × 3361 × 4021 = 824389441 </pre> =={{header\|PARI/GP}}== <syntaxhighlight lang="parigp">f(p)={ my(v=List(),q,r); for(h=2,p-1, Line 2,130 ⟶ 2,438: {{out}} <pre>561, 1105, 2465, 10585, 1729, 2821, 6601, 8911, 15841, 52633, 29341, 46657, 115921, 314821, 530881, 162401, 7207201, 334153, 1024651, 1615681, 3581761, 5444489, 399001, 512461, 1193221, 1857241, 5049001, 5481451, 471905281, 294409, 488881, 1461241, 8134561, 36765901, 252601, 410041, 1909001, 5148001, 7519441, 434932961, 2489462641, 1152271, 3057601, 5968873, 6868261, 11972017, 14913991, 15829633, 43331401, 67902031, 368113411, 564651361, 104569501, 902645857, 958762729, 2508013, 4335241, 17316001, 178837201, 6189121, 9439201, 15247621, 35703361, 60957361, 99036001, 101649241, 329769721, 824389441, 1574601601, 10267951, 163954561, 7991602081,</pre> =={{header\|Perl}}== {{libheader\|ntheory}} <syntaxhighlight lang="perl">use ntheory qw/forprimes is_prime vecprod/; forprimes { my $p = $_; Line 2,162 ⟶ 2,469: 61 x 3361 x 4021 = 824389441 </pre> =={{header\|Phix}}== <!--<syntaxhighlight lang=~~Phix~~"phix">(phixonline)--> <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> Line 2,204 ⟶ 2,510: 69 Carmichael numbers found </pre> =={{header\|PicoLisp}}== <syntaxhighlight lang=~~PicoLisp~~"picolisp">(de modulo (X Y) (% (+ Y (% X Y)) Y) ) Line 2,246 ⟶ 2,551: (bye)</syntaxhighlight> =={{header\|PL/I}}== <syntaxhighlight lang=PL"pl/Ii">Carmichael: procedure options (main, reorder); /* 24 January 2014 / declare (Prime1, Prime2, Prime3, h3, d) fixed binary (31); Line 2,371 ⟶ 2,675: 61 x 3361 x 4021 </pre> =={{header\|Prolog}}== <syntaxhighlight lang="prolog"> show(Limit) :- forall( Line 2,522 ⟶ 2,825: true. </pre> =={{header\|Python}}== <syntaxhighlight lang="python">class Isprime(): ''' Extensible sieve of Eratosthenes Line 2,610 ⟶ 2,912: (61, 181, 5521), (61, 241, 421), (61, 271, 571), (61, 277, 2113), (61, 421, 12841), (61, 541, 3001), (61, 661, 2521), (61, 1301, 19841), (61, 3361, 4021)</pre> =={{header\|Racket}}== <syntaxhighlight lang="racket"> #lang racket (require math) Line 2,631 ⟶ 2,932: </syntaxhighlight> Output: <syntaxhighlight lang="racket"> (3 11 17 => 561) (5 29 73 => 10585) Line 2,695 ⟶ 2,996: (61 3361 4021 => 824389441) </syntaxhighlight> =={{header\|Raku}}== (formerly Perl 6) {{works with\|Rakudo\|2015.12}} An almost direct translation of the pseudocode. We take the liberty of going up to 67 to show we aren't limited to 32-bit integers. (Raku uses arbitrary precision in any case.) <syntaxhighlight lang="raku" line>for (2..67).grep: .is-prime -> \Prime1 { for 1 ^..^ Prime1 -> \h3 { my \g = h3 + Prime1; Line 2,788 ⟶ 3,088: 67 × 331 × 7393 == 163954561 67 × 331 × 463 == 10267951</pre> =={{header\|REXX}}== Note that REXX's version of   '''modulus'''   (<big><code>'''//'''</code></big>)   is really a   ''remainder''   function. Line 2,795 ⟶ 3,094: Some code optimization was done, while not necessary for the small default number ('''61'''),   it was significant for larger numbers. <syntaxhighlight lang="rexx">/REXX program calculates Carmichael 3─strong pseudoprimes (up to and including N). / numeric digits 18 /handle big dig #s (9 is the default)./ parse arg N .; if N=='' \| N=="," then N=61 /allow user to specify for the search./ Line 2,866 ⟶ 3,165: ──────── 8716 Carmichael numbers found. </pre> =={{header\|Ring}}== <syntaxhighlight lang="ring"> # Project : Carmichael 3 strong pseudoprimes Line 2,987 ⟶ 3,285: 61 241 421 6189121 61 3361 4021 824389441 </pre> =={{header\|RPL}}== {{works with\|HP\|49}} « { } 3 ROT '''FOR''' p1 2 p1 1 - '''FOR''' h3 1 h3 p1 + 1 - '''FOR''' d '''IF''' h3 p1 + p1 1 - * d MOD NOT p1 SQ NEG h3 MOD d h3 MOD == AND '''THEN''' p1 1 - h3 p1 + d IQUOT * 1 + '''CASE''' DUP ISPRIME? NOT '''THEN''' DROP '''END''' p1 OVER * h3 IQUOT 1 + DUP ISPRIME? NOT '''THEN''' DROP2 '''END''' DUP2 * p1 1 - MOD 1 ≠ '''THEN''' DROP2 '''END''' p1 UNROT 3 →LIST 1 →LIST + '''END''' '''END''' '''NEXT''' '''NEXT''' p1 NEXTPRIME 1 - 'p1' STO '''NEXT''' » '<span style="color:blue">CARMIC</span>' STO 61 <span style="color:blue">CARMIC</span> {{out}} <pre> 1: { { 3 11 17 } { 5 29 73 } { 5 17 29 } { 5 13 17 } { 7 19 67 } { 7 31 73 } { 7 13 31 } { 7 73 103 } { 7 13 19 } { 13 61 397 } { 13 37 241 } { 13 97 421 } { 13 37 97 } { 13 37 61 } { 17 353 1201 } { 19 199 271 } { 23 199 353 } { 29 113 1093 } { 29 197 953 } { 31 991 15361 } { 31 61 631 } { 31 151 1171 } { 31 61 271 } { 31 61 211 } { 31 271 601 } { 31 181 331 } { 37 109 2017 } { 37 73 541 } { 37 613 1621 } { 37 73 181 } { 37 73 109 } { 41 1721 35281 } { 41 881 12041 } { 41 241 761 } { 41 241 521 } { 43 631 13567 } { 43 127 2731 } { 43 127 1093 } { 43 211 757 } { 43 631 1597 } { 43 127 211 } { 43 211 337 } { 43 547 673 } { 43 3361 3907 } { 47 3359 6073 } { 47 1151 1933 } { 47 3727 5153 } { 53 53 937 } { 53 157 2081 } { 53 157 521 } { 59 1451 2089 } { 61 421 12841 } { 61 181 5521 } { 61 61 1861 } { 61 61 1861 } { 61 181 1381 } { 61 541 3001 } { 61 661 2521 } { 61 241 421 } { 61 3361 4021 } } </pre> =={{header\|Ruby}}== {{works with\|Ruby\|1.9}} <syntaxhighlight lang="ruby"># Generate Charmichael Numbers require 'prime' Line 3,100 ⟶ 3,425: =={{header\|Rust}}== <syntaxhighlight lang="rust"> fn is_prime(n: i64) -> bool { if n > 1 { Line 3,167 ⟶ 3,492: (61, 3361, 4021) </pre> =={{header\|Seed7}}== The function [http://seed7.sourceforge.net/algorith/math.htm#isPrime isPrime] below is borrowed from the [http://seed7.sourceforge.net/algorith Seed7 algorithm collection]. <syntaxhighlight lang="seed7">$ include "seed7_05.s7i"; const func boolean: isPrime (in integer: number) is func Line 3,292 ⟶ 3,616: 61 * 3361 * 4021 = 824389441 </pre> =={{header\|Sidef}}== {{trans\|Perl}} <syntaxhighlight lang="ruby">func forprimes(a, b, callback) { for (a = (a-1 -> next_prime); a <= b; a.next_prime!) { callback(a) Line 3,329 ⟶ 3,652: 61 x 3361 x 4021 = 824389441 </pre> =={{header\|Swift}}== {{trans\|Rust}} <syntaxhighlight lang="swift">import Foundation extension BinaryInteger { Line 3,417 ⟶ 3,739: (61, 241, 421) (61, 3361, 4021)</pre> =={{header\|Tcl}}== Using the primality tester from [[Miller-Rabin primality test#Tcl\|the Miller-Rabin task]]... <syntaxhighlight lang="tcl">proc carmichael {limit {rounds 10}} { set carmichaels {} for {set p1 2} {$p1 <= $limit} {incr p1} { Line 3,444 ⟶ 3,765: }</syntaxhighlight> Demonstrating: <syntaxhighlight lang="tcl">set results [carmichael 61 2] puts "[expr {[llength $results]/4}] Carmichael numbers found" foreach {p1 p2 p3 c} $results { Line 3,522 ⟶ 3,843: 61 x 3361 x 4021 = 824389441 </pre> =={{header\|Vala}}== {{trans\|D}} <syntaxhighlight lang="vala">long mod(long n, long m) { return ((n % m) + m) % m; } Line 3,659 ⟶ 3,979: 61 × 3361 × 4021 = 824389441 </pre> =={{header\|Wren}}== {{trans\|Go}} {{libheader\|Wren-fmt}} {{libheader\|Wren-math}} <syntaxhighlight lang=~~ecmascript~~"wren">import "./fmt" for Fmt import "./math" for Int var mod = Fn.new { \|n, m\| ((n%m) + m) % m } Line 3,774 ⟶ 4,093: =={{header\|zkl}}== Using the Miller-Rabin primality test in lib GMP. <syntaxhighlight lang="zkl">var BN=Import("zklBigNum"), bi=BN(0); // gonna recycle bi primes:=T(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61); var p2,p3; Line 3,786 ⟶ 4,105: ]]; fcn mod(a,b) { m:=a%b; if(m<0) m+b else m }</syntaxhighlight> <syntaxhighlight lang="zkl">cs.len().println(" Carmichael numbers found:"); cs.pump(Console.println,fcn([(p1,p2,p3)]){ "%2d * %4d * %5d = %d".fmt(p1,p2,p3,p1p2p3) });</syntaxhighlight> Line 3,805 ⟶ 4,124: 61 * 3361 * 4021 = 824389441 </pre> ~~=={{header\|ZX Spectrum Basic}}==~~ ~~{{trans\|C}}~~ ~~<syntaxhighlight lang=zxbasic>10 FOR p=2 TO 61~~ ~~20 LET n=p: GO SUB 1000~~ ~~30 IF NOT n THEN GO TO 200~~ ~~40 FOR h=1 TO p-1~~ ~~50 FOR d=1 TO h-1+p~~ ~~60 IF NOT (FN m((h+p)(p-1),d)=0 AND FN w(-pp,h)=FN m(d,h)) THEN GO TO 180~~ ~~70 LET q=INT (1+((p-1)(h+p)/d))~~ ~~80 LET n=q: GO SUB 1000~~ ~~90 IF NOT n THEN GO TO 180~~ ~~100 LET r=INT (1+(pq/h))~~ ~~110 LET n=r: GO SUB 1000~~ ~~120 IF (NOT n) OR ((FN m((qr),(p-1))<>1)) THEN GO TO 180~~ ~~130 PRINT p;" ";q;" ";r~~ ~~180 NEXT d~~ ~~190 NEXT h~~ ~~200 NEXT p~~ ~~210 STOP~~ ~~1000 IF n<4 THEN LET n=(n>1): RETURN~~ ~~1010 IF (NOT FN m(n,2)) OR (NOT FN m(n,3)) THEN LET n=0: RETURN~~ ~~1020 LET i=5~~ ~~1030 IF NOT ((ii)<=n) THEN LET n=1: RETURN~~ ~~1040 IF (NOT FN m(n,i)) OR NOT FN m(n,(i+2)) THEN LET n=0: RETURN~~ ~~1050 LET i=i+6~~ ~~1060 GO TO 1030~~ ~~2000 DEF FN m(a,b)=a-(INT (a/b)*b): REM Mod function~~ ~~2010 DEF FN w(a,b)=FN m(FN m(a,b)+b,b): REM Mod function modified~~ ~~</syntaxhighlight>~~