Data update
This commit is contained in:
Ingy döt Net
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1853 changed files with 35514 additions and 9441 deletions
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function isProbablyPrime(n as *BigInteger, k as long) {
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boolean T=true, F=false
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=F
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Zero=BigInteger("0")
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One=BigInteger("1")
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Two=BigInteger("2")
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Method n, "compare", Two as c1
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Method n, "modulus", Two as m2
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method m2,"compare", zero as C2
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if c1=0 or c2=0 then exit
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with n, "toString" as ns$
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s=0
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Method n, "subtract", one as nn
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d=nn
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with d, "tostring" as dstr$
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do
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method d,"modulus", two as m2
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method m2,"compare", zero as C
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if c else exit
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s++
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method d, "divide", two as d
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Always
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z=len(ns$)
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a=one
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with a, "toString" as astr$
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x=a
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=T
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for i=1 to k {
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do
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zs=""
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for j=1 to len(ns$)
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zs+=chr$(47+random(1,10))
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next
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a=bigInteger(zs)
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method nn,"compare", a as C
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method a,"compare", one as c1
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until c=1 and c1>-1
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method a, "modpow", d, n as x
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method x,"compare", one as c1
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if c1 else continue
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method x,"compare", nn as c1
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if c1 else continue
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for r=1 to s {
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method x, "modpow", two, n as x
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method x,"compare", one as c1
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if c1 else =F : break
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method x,"compare", nn as c1
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if c1 else exit
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}
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if c1 then =F: break
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}
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}
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profiler
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Print isProbablyPrime(BigInteger("5400349"), 5)=True
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print timecount
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profiler
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a=BigInteger("5400349"): Method a, "isProbablyPrime", 5 as ret:Print ret
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print timecount
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@ -0,0 +1,57 @@
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uses System.Security.Cryptography;
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function IsProbablePrime(source: biginteger; certainty: integer): boolean;
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begin
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if (source = 2) or (source = 3) then
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begin result := true; exit end;
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if (source < 2) or (source mod 2 = 0) then
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begin result := false; exit end;
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var d := source - 1;
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var s := 0;
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while d mod 2 = 0 do
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begin
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d := d div 2;
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s += 1;
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end;
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var rng := RandomNumberGenerator.Create();
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var bytes := new byte[source.ToByteArray.LongLength];
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var a: biginteger;
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loop certainty do
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begin
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repeat
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rng.GetBytes(bytes);
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a := new BigInteger(bytes);
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until (a >= 2) and (a < source - 2);
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var x := BigInteger.ModPow(a, d, source);
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if (x = 1) or (x = source - 1) then continue;
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for var r := 1 to s - 1 do
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begin
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x := BigInteger.ModPow(x, 2, source);
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if x = 1 then
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begin result := false; exit end;
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if x = source - 1 then break;
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end;
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if x <> source - 1 then
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begin result := false; exit end;
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end;
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result := true;
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end;
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begin
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var data := |'4547337172376300111955330758342147474062293202868155909489',
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'4547337172376300111955330758342147474062293202868155909393'|;
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foreach var candidate in data do
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isprobableprime(candidate.tobiginteger, 10).Println;
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foreach var x in (900..1000) do
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if isprobableprime(x, 10) then print(x);
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end.
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@ -1,48 +0,0 @@
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/*REXX program puts the Miller─Rabin primality test through its paces. */
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parse arg limit times seed . /*obtain optional arguments from the CL*/
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if limit=='' | limit=="," then limit= 1000 /*Not specified? Then use the default.*/
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if times=='' | times=="," then times= 10 /* " " " " " " */
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if datatype(seed, 'W') then call random ,,seed /*If seed specified, use it for RANDOM.*/
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numeric digits max(200, 2*limit) /*we're dealing with some ginormous #s.*/
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tell= times<0 /*display primes only if times is neg.*/
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times= abs(times); w= length(times) /*use absolute value of TIMES; get len.*/
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call genP limit /*suspenders now, use a belt later ··· */
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@MR= 'Miller─Rabin primality test' /*define a character literal for SAY. */
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say "There are" # 'primes ≤' limit /*might as well display some stuff. */
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say /* [↓] (skipping unity); show sep line*/
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do a=2 to times; say copies('─', 89) /*(skipping unity) do range of TIMEs.*/
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p= 0 /*the counter of primes for this pass. */
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do z=1 for limit /*now, let's get busy and crank primes.*/
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if \M_Rt(z, a) then iterate /*Not prime? Then try another number.*/
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p= p + 1 /*well, we found another one, by gum! */
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if tell then say z 'is prime according to' @MR "with K="a
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if !.z then iterate
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say '[K='a"] " z "isn't prime !" /*oopsy─doopsy and/or whoopsy─daisy !*/
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end /*z*/
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say ' for 1──►'limit", K="right(a,w)',' @MR "found" p 'primes {out of' #"}."
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end /*a*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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genP: parse arg high; @.=0; @.1=2; @.2=3; !.=@.; !.2=1; !.3=1; #=2
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do j=@.#+2 by 2 to high /*just examine odd integers from here. */
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do k=2 while k*k<=j; if j//@.k==0 then iterate j; end /*k*/
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#= # + 1; @.#= j; !.j= 1 /*bump prime counter; add prime to the */
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end /*j*/; return /*@. array; define a prime in !. array.*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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M_Rt: procedure; parse arg n,k; d= n-1; nL=d /*Miller─Rabin: A.K.A. Rabin─Miller.*/
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if n==2 then return 1 /*special case of (the) even prime. */
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if n<2 | n//2==0 then return 0 /*check for too low, or an even number.*/
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do s=-1 while d//2==0; d= d % 2 /*keep halving until a zero remainder.*/
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end /*while*/
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do k; ?= random(2, nL) /* [↓] perform the DO loop K times.*/
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x= ?**d // n /*X can get real gihugeic really fast.*/
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if x==1 | x==nL then iterate /*First or penultimate? Try another pow*/
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do s; x= x**2 // n /*compute new X ≡ X² modulus N. */
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if x==1 then return 0 /*if unity, it's definitely not prime.*/
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if x==nL then leave /*if N-1, then it could be prime. */
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end /*r*/ /* [↑] // is REXX's division remainder*/
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if x\==nL then return 0 /*nope, it ain't prime nohows, noway. */
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end /*k*/ /*maybe it's prime, maybe it ain't ··· */
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return 1 /*coulda/woulda/shoulda be prime; yup.*/
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@ -1,90 +0,0 @@
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include Settings
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say version; say 'Miller-Rabin primality test'; say
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numeric digits 1000
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say '25 numbers of the form 2^n-1, mostly Mersenne primes'
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say 'Up to about 25 digits deterministic, above probabilistic'
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say
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mm = '2 3 5 7 11 13 17 19 23 31 61 89 97 107 113 127 131 521 ',
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|| '607 1279 2203 2281 2293 3217 3221'
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do nn = 1 to 25
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a = Word(mm,nn); b = 2**a-1; l = Length(b)
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call Time('r'); p = IsPrime(b); e = Time('e')
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if l > 20 then
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b = Left(b,10)'...'Right(b,10)
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select
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when p = 0 then
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p = 'not'
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when l < 26 then
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p = 'for sure'
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otherwise
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p = 'probable'
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end
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say '2^'a'-1' '=' b '('l' digits) is' p 'prime' '('Format(e,,3) 'seconds)'
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end
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return
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IsPrime:
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/* Is a number prime? */
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procedure expose glob.
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arg x
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/* Low primes also used as deterministic witnesses */
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w1 = ' 2 3 5 7 11 13 17 19 23 29 31 37 41 '
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/* Fast values */
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w = x
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if Pos(' 'w' ',w1) > 0 then
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return 1
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if x//2 = 0 then
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return 0
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if x//3 = 0 then
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return 0
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if Right(x,1) = 5 then
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return 0
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/* Miller-Rabin primality test */
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numeric digits 2*Length(x)
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d = x-1; e = d
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/* Reduce n-1 by factors of 2 */
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do s = -1 while d//2 = 0
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d = d%2
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end
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/* Thresholds deterministic witnesses */
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w2 = '2047 1373653 25326001 3215031751 2152302898747 3474749660383 341550071728321 ',
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|| '0 3825123056546413051 0 0 318665857834031151167461 3317044064679887385961981 '
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w = Words(w2)
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/* Up to 13 deterministic trials */
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if x < Word(w2,w) then do
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do k = 1 to w
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if x < Word(w2,k) then
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leave
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end
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end
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/* or 3 probabilistic trials */
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else do
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w1 = ' '
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do k = 1 to 3
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r = Rand(2,e)/1; w1 = w1||r||' '
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end
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k = k-1
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end
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/* Algorithm using generated witnesses */
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do k = 1 to k
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a = Word(w1,k); y = Powermod(a,d,x)
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if y = 1 then
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iterate
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if y = e then
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iterate
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do s
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y = (y*y)//x
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if y = 1 then
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return 0
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if y = e then
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leave
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end
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if y <> e then
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return 0
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end
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return 1
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include Functions
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include Numbers
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include Abend
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@ -0,0 +1,29 @@
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include Settings
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say version; say 'Miller-Rabin primality test'; say
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numeric digits 1000
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say '25 numbers of the form 2^n-1, mostly Mersenne primes'
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say 'Up to about 25 digits deterministic, above probabilistic'
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say
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mm = '2 3 5 7 11 13 17 19 23 31 61 89 97 107 113 127 131 521 ',
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|| '607 1279 2203 2281 2293 3217 3221'
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do nn = 1 to 25
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a = Word(mm,nn); b = 2**a-1; l = Length(b)
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call Time('r'); p = Prime(b); e = Time('e')
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if l > 20 then
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b = Left(b,10)'...'Right(b,10)
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select
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when p = 0 then
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p = 'not'
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when l < 26 then
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p = 'for sure'
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otherwise
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p = 'probable'
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end
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say '2^'a'-1' '=' b '('l' digits) is' p 'prime' '('Format(e,,3) 'seconds)'
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end
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return
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include Functions
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include Numbers
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include Abend
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