for n being Element of NAT st 1 < n & n * n <= 337 & n is prime holds
not n divides 337

proof

let n be Element of NAT ; :: thesis: ( 1 < n & n * n <= 337 & n is prime implies not n divides 337 )
337 = (2 * 168) + 1 ;
then A1: not 2 divides 337 ;
337 = (3 * 112) + 1 ;
then A2: not 3 divides 337 by NAT_4:9;
337 = (5 * 67) + 2 ;
then A3: not 5 divides 337 by NAT_4:9;
337 = (7 * 48) + 1 ;
then A4: not 7 divides 337 by NAT_4:9;
337 = (11 * 30) + 7 ;
then A5: not 11 divides 337 by NAT_4:9;
337 = (13 * 25) + 12 ;
then A6: not 13 divides 337 by NAT_4:9;
337 = (17 * 19) + 14 ;
then A7: not 17 divides 337 by NAT_4:9;
337 = (19 * 17) + 14 ;
then A8: not 19 divides 337 by NAT_4:9;
337 = (23 * 14) + 15 ;
then not 23 divides 337 by NAT_4:9;
hence ( 1 < n & n * n <= 337 & n is prime implies not n divides 337 ) by A1, A2, A3, A4, A5, A6, A7, A8, NAT_4:62; :: thesis: verum

end;

hence 337 is prime by NAT_4:14; :: thesis: verum