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


program primes;
 
function prime(n: integer): boolean;
var
  i: integer; max: real;
begin
  if n = 2 then
    prime := true
  else if (n <= 1) or (n mod 2 = 0) then
    prime := false
  else begin
    prime := true; i := 3; max := sqrt(n);
    while i <= max do begin
      if n mod i = 0 then begin
        prime := false; exit
      end;
      i := i + 2
    end
  end
end;
 
{ Test and display primes 0 .. 50 }
var 
  n: integer;
begin
  for n := 0 to 50 do
    if (prime(n)) then
      write(n, ' ');
end.