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


declare @number int
set @number = 514229 -- number to check
 
;with cte(number) as 
(
 select 2
 union all
 select number+1
 from cte
 where number+1 < @number
)
select
      cast(@number as varchar(100)) +
      case 
          when exists
				  (
					select * 
					from 
					(
						select number, @number % number modNumber
						from cte
					) tmp
					where tmp.modNumber = 0 
				  ) 
				          then ' is composite'
		  else
						 ' is prime'
	  end primalityTest
option (maxrecursion 0)