Problem Statement

Generate a sequence of primes by means of trial division.

Trial division is an algorithm where a candidate number is tested for being a prime by trying to divide it by other numbers. You may use primes, or any numbers of your choosing, as long as the result is indeed a sequence of primes. The sequence may be bounded (i.e. up to some limit), unbounded, starting from the start (i.e. 2) or above some given value. Organize your function as you wish, in particular, it might resemble a filtering operation, or a sieving operation. If you want to use a ready-made is_prime function, use one from the Primality by trial division page (i.e., add yours there if it isn't there already).

Let's start with the solution:

(defun primes-up-to (max-number)
    "Compute all primes up to MAX-NUMBER using trial division"
    (loop for n from 2 upto max-number
          when (notany (evenly-divides n) primes)
          collect n into primes
          finally (return primes)))
     
(defun evenly-divides (n)
    "Create a function that checks whether its input divides N evenly"
    (lambda (x) (integerp (/ n x))))
     
(print (primes-up-to 100))