937 = (2 * 468) + 1 ;
hence not 2 divides 937 by NAT_4:9; :: thesis:
937 = (3 * 312) + 1 ;
hence not 3 divides 937 by NAT_4:9; :: thesis:
937 = (5 * 187) + 2 ;
hence not 5 divides 937 by NAT_4:9; :: thesis:
937 = (7 * 133) + 6 ;
hence not 7 divides 937 by NAT_4:9; :: thesis:
937 = (11 * 85) + 2 ;
hence not 11 divides 937 by NAT_4:9; :: thesis:
937 = (13 * 72) + 1 ;
hence not 13 divides 937 by NAT_4:9; :: thesis:
937 = (17 * 55) + 2 ;
hence not 17 divides 937 by NAT_4:9; :: thesis:
937 = (19 * 49) + 6 ;
hence not 19 divides 937 by NAT_4:9; :: thesis:
937 = (23 * 40) + 17 ;
hence not 23 divides 937 by NAT_4:9; :: thesis:
937 = (29 * 32) + 9 ;
hence not 29 divides 937 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 937 & n is prime holds
not n divides 937 by XPRIMET1:20;
hence 937 is prime by NAT_4:14; :: thesis: