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


function isprime_trialdivision{T<:Integer}(n::T)
    1 < n || return false
    n != 2 || return true
    isodd(n) || return false
    for i in 3:isqrt(n)
        n%i != 0 || return false
    end
    return true
end
 
n = 100
a = filter(isprime_trialdivision, [1:n])
 
if all(a .== primes(n))
    println("The primes <= ", n, " are:\n    ", a)
else
    println("The function does not accurately calculate primes.")
end