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
  =   incs n I inc
    .   4 2 4 2 4 6 2 6:?incs
      & 2:?n
      & 1 2 2 !incs:?I
      &   whl
        ' ( !n*!n:~>!arg
          & div$(!arg.!n)*!n:~!arg
          & (!I:%?inc ?I|!incs:%?inc ?I)
          & !n+!inc:?n
          )
      & !n*!n:>!arg
  )
& 100000000000:?p
&   whl
  ' ( !p+1:<100000000100:?p
    & (   prime$!p
        & out$!p
      | 
      )
    )
& ;