Task

Write a boolean function that tells whether a given integer is prime.



Remember that   1   and all non-positive numbers are not prime.

Use trial division.

Even numbers greater than   2   may be eliminated right away.

A loop from   3   to   √ n    will suffice,   but other loops are allowed.



Related tasks

   count in factors
   prime decomposition
   AKS test for primes
   factors of an integer
   Sieve of Eratosthenes
   factors of a Mersenne number
   trial factoring of a Mersenne number
   partition an integer X into N primes
   sequence of primes by Trial Division


prime(2).
prime(N) :- 
  between(3, inf, N),
  1 is N mod 2,             % odd
  M is floor(sqrt(N+1)),    % round-off paranoia 
  Max is (M-1) // 2,        % integer division
  forall( between(1, Max, I), N mod (2*I+1) > 0 ).