Lucas-Lehmer test: Difference between revisions
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and only if 2**p-1 divides S(p-1) where S(n+1)=S(n)**2-2, and S(1)=4.
The following programs calculate
=={{header|ALGOL 68}}==
Interpretor: algol68g-mk11
main:(
PRAGMAT stack=1M precision=20001 PRAGMAT
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IF p = 2 THEN TRUE
ELSE
LONG LONG INT m p = LONG LONG 2 ** p - 1,
FROM 3 TO p DO
s := (s * s - 2) MOD m p
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FI;
INT upb =
printf(($" Finding Mersenne primes in M[2.."g(0)"]: "l$,upb));
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else {
BOOL prime = TRUE;
const int to = sqrt(p);
int i;
for(i = 3; i <= to; i+=2)
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if( p == 2 ) return TRUE;
else {
const long long unsigned m_p = ( 1LLU << p ) - 1;
long long unsigned s = 4;
int i;
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int main(int argc, char **argv){
const int upb = log2l(ULLONG_MAX)/2;
int p;
printf(" Mersenne primes:\n");
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Revision as of 17:08, 15 February 2008
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You are encouraged to solve this task according to the task description, using any language you may know.
Lucas-Lehmer Test: for p a prime, the Mersenne number 2**p-1 is prime if and only if 2**p-1 divides S(p-1) where S(n+1)=S(n)**2-2, and S(1)=4.
The following programs calculate all Mersenne primes up to the implementation precision.
ALGOL 68
Interpretor: algol68g-mk11
main:( PRAGMAT stack=1M precision=20001 PRAGMAT PROC is prime = ( INT p )BOOL: IF p = 2 THEN TRUE ELIF p <= 1 OR p MOD 2 = 0 THEN FALSE ELSE BOOL prime := TRUE; FOR i FROM 3 BY 2 TO ENTIER sqrt(p) WHILE prime := p MOD i /= 0 DO SKIP OD; prime FI; PROC is mersenne prime = ( INT p )BOOL: IF p = 2 THEN TRUE ELSE LONG LONG INT m p = LONG LONG 2 ** p - 1, s := 4; FROM 3 TO p DO s := (s * s - 2) MOD m p OD; s = 0 FI; INT upb = ENTIER(SHORTEN long log(SHORTEN LONG LONG REAL(long long max int))/log(2)/2); printf(($" Finding Mersenne primes in M[2.."g(0)"]: "l$,upb)); FOR p FROM 2 TO upb DO IF is prime(p) THEN IF is mersenne prime(p) THEN printf (($" M"g(0)$,p)) FI FI OD )
Output:
Finding Mersenne primes in M[2..33253]: M2 M3 M5 M7 M13 M17 M19 M31 M61 M89 M107 M127 M521 M607 M1279 M2203 M2281 M3217 M4253 M4423 M9689 M9941 M11213 M19937 M21701 M23209
See also: http://www.xs4all.nl/~jmvdveer/mersenne.a68.html
C
#include <math.h> #include <stdio.h> #include <limits.h> #pragma precision=log10l(ULLONG_MAX)/2 typedef enum { FALSE=0, TRUE=1 } BOOL; BOOL is_prime( int p ){ if( p == 2 ) return TRUE; else if( p <= 1 || p % 2 == 0 ) return FALSE; else { BOOL prime = TRUE; const int to = sqrt(p); int i; for(i = 3; i <= to; i+=2) if (!(prime = p % i))break; return prime; } } BOOL is_mersenne_prime( int p ){ if( p == 2 ) return TRUE; else { const long long unsigned m_p = ( 1LLU << p ) - 1; long long unsigned s = 4; int i; for (i = 3; i <= p; i++){ s = (s * s - 2); s = s % m_p; } return s == 0; } } int main(int argc, char **argv){ const int upb = log2l(ULLONG_MAX)/2; int p; printf(" Mersenne primes:\n"); for( p = 2; p <= upb; p += 1 ){ if( is_prime(p) && is_mersenne_prime(p) ){ printf (" M%u",p); } } printf("\n"); }
Compiler version: gcc version 4.1.2 20070925 (Red Hat 4.1.2-27)
Compiler options: gcc -std=c99 -lm Lucas-Lehmer_test.c -o Lucas-Lehmer_test
Output:
Mersenne primes: M2 M3 M5 M7 M13 M17 M19 M31