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


% returns true if n is prime, false otherwise %
% uses trial division                         %
logical procedure isPrime ( integer value n ) ;
    if n < 3 or not odd( n ) then n = 2
    else begin
        % odd number > 2 %
        integer f, rootN;
        logical havePrime;
        f         := 3;
        rootN     := entier( sqrt( n ) );
        havePrime := true;
        while f <= rootN and havePrime do begin
            havePrime := ( n rem f ) not = 0;
            f         := f + 2
        end;
        havePrime
    end isPrime ;