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


#lang racket
 
(define (prime? number)
  (cond ((not (positive? number)) #f)
        ((= 1 number) #f)
        ((even? number) (= 2 number))
        (else (for/and ((i (in-range 3 (ceiling (sqrt number)))))
                (not (zero? (remainder number i)))))))