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


TrialDivision := proc( n :: integer )
        if n <= 1 then
                false
        elif n = 2 then
                true
        elif type( n, 'even' ) then
                false
        else
                for local i from 3 by 2 while i * i <= n do
                        if irem( n, i ) = 0 then
                                return false
                        end if
                end do;
                true
        end if
end proc: