Lucas-Lehmer test: Difference between revisions
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conducive to find large primes. |
conducive to find large primes. |
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<lang rexx>/*REXX program to use Lucas-Lehmer primality test for prime powers of 2.*/ |
<lang rexx>/*REXX program to use Lucas-Lehmer primality test for prime powers of 2.*/ |
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parse arg limit . /*get the argument (if any). */ |
parse arg limit . /*get the argument (if any). */ |
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if limit=='' then limit=1000 /*if no argument, assume 1000. */ |
if limit=='' then limit=1000 /*if no argument, assume 1000. */ |
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do j=1 by 2 to limit /*only process so much... */ |
do j=1 by 2 to limit /*only process so much... */ |
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/*there're only so many hours in a day...*/ |
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power=j |
power=j |
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if j==1 then power=2 /*special case for the even prime*/ |
if j==1 then power=2 /*special case for the even prime*/ |
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if \isprime(power) then iterate /*if not prime, then ignore it. */ |
if \isprime(power) then iterate /*if not prime, then ignore it. */ |
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list=list Lucas_Lehmer2(power) /*add to list (or maybe not). */ |
list=list Lucas_Lehmer2(power) /*add to list (or maybe not). */ |
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end /*j*/ |
end /*j*/ |
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list=space(list) /*remove extraneous blanks. */ |
list=space(list) /*remove extraneous blanks. */ |
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say; say center('list',60-3,"═") /*show a fancy-dancy header/title*/ |
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say |
say |
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do k=1 for words(list) /*show entries in list, 1/line. */ |
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say |
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do j=1 for words(list) /*show entries in list, 1/line. */ |
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end |
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say |
say |
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exit |
exit |
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/*──────────────────────────────────LUCAS_LEHMER2 subroutine────────────*/ |
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/*-------------------------------------LUCAS_LEHMER2 subroutine---------*/ |
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Lucas_Lehmer2: procedure; parse arg ? /*Lucas-Lehmer test on 2**? - 1 */ |
Lucas_Lehmer2: procedure; parse arg ? /*Lucas-Lehmer test on 2**? - 1 */ |
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numeric form /*ensure correct scientific form.*/ |
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if ?==2 then s=0 |
if ?==2 then s=0 |
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else s=4 |
else s=4 |
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/* DIGITs of 1 million could be used, but that really */ |
/* DIGITs of 1 million could be used, but that really */ |
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/* slows up the whole works. So, we start with the */ |
/* slows up the whole works. So, we start with the */ |
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q=2**?-1 /*now, compute the real McCoy. */ |
q=2**?-1 /*now, compute the real McCoy. */ |
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s=(s*s-2)//q /*modulus in REXX is: // */ |
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end |
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if s\==0 then return '' /*return nuttin' if not prime. */ |
if s\==0 then return '' /*return nuttin' if not prime. */ |
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return 'M'? /*return modified (prime) number.*/ |
return 'M'? /*return modified (prime) number.*/ |
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/*──────────────────────────────────ISPRIME subroutine──────────────────*/ |
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/*-------------------------------------ISPRIME subroutine---------------*/ |
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isprime: procedure; parse arg x; if x<2 then return 0 |
isprime: procedure; parse arg x; if x<2 then return 0 /*idiot test.*/ |
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if wordpos(x,'2 3 5 7')\==0 then return 1 /*test for special cases.*/ |
if wordpos(x,'2 3 5 7')\==0 then return 1 /*test for special cases.*/ |
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if x//3==0 then return 0 /*divisible by three? Not prime.*/ |
if x//3==0 then return 0 /*divisible by three? Not prime.*/ |
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end /*j*/</lang> |
end /*j*/</lang> |
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'''output''' when the following is used: <tt> 10000 </tt> |
'''output''' when the following is used: <tt> 10000 </tt> |
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<pre style=" |
<pre style="overflow:scroll"> |
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══════════════════════════list═══════════════════════════ |
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--------------------------list--------------------------- |
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M2 |
M2 |
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