Name

number_pseudoprime — Check if a number is a pseudo prime.

Calling Sequence

   isprime = number_pseudoprime ( n )
   isprime = number_pseudoprime ( n , a )
   
   

Parameters

n :

a 1x1 matrix of floating point integers, the number to test for primality, must be positive

a :

a 1x1 matrix of floating point integers, the base (default 2), must be positive

isprime :

a 1x1 matrix of booleans

Description

Returns %f if the number is composite. Returns %t if the number is a base-a pseudo-prime, in which case the number n may be either prime or pseudo-prime. A base-a pseudo prime is so that a^(n-1) = 1 (mod n).

Examples

// Check for actual primes
number_pseudoprime ( 7 ) // %t
number_pseudoprime ( 5 ) // %t
number_pseudoprime ( 5 , 3 ) // %t
// Check for composite numbers
number_pseudoprime ( 10 ) // %f
number_pseudoprime ( 20 ) // %f
// Check for pseudo-primes : this is a known limitation of the test
// 341 = 11 * 31
number_pseudoprime ( 341 ) // %t
number_pseudoprime ( 561 ) // %t
number_pseudoprime ( 645 ) // %t
number_pseudoprime ( 1105 ) // %t

   

Authors

Copyright (C) 2009 - 2010 - DIGITEO - Michael Baudin