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


over : 2 pick
 2dup : over over
 even? : 1 & 0 =
 
 # trial n d yields "n d 0/1 false" or "n d+2 true"
 trial : 2 +                 true
 trial : 2dup % 0 =   then 0 false
 trial : 2dup dup * < then 1 false
 trial-loop : trial &repeat
 
 # prime? n yields flag
 prime? : 3 trial-loop >flag drop drop
 prime? : dup even? then drop false
 prime? : dup 2 =   then drop true
 prime? : dup 2 <   then drop false