3329 = (2 * 1664) + 1 ;
hence not 2 divides 3329 by NAT_4:9; :: thesis:
3329 = (3 * 1109) + 2 ;
hence not 3 divides 3329 by NAT_4:9; :: thesis:
3329 = (5 * 665) + 4 ;
hence not 5 divides 3329 by NAT_4:9; :: thesis:
3329 = (7 * 475) + 4 ;
hence not 7 divides 3329 by NAT_4:9; :: thesis:
3329 = (11 * 302) + 7 ;
hence not 11 divides 3329 by NAT_4:9; :: thesis:
3329 = (13 * 256) + 1 ;
hence not 13 divides 3329 by NAT_4:9; :: thesis:
3329 = (17 * 195) + 14 ;
hence not 17 divides 3329 by NAT_4:9; :: thesis:
3329 = (19 * 175) + 4 ;
hence not 19 divides 3329 by NAT_4:9; :: thesis:
3329 = (23 * 144) + 17 ;
hence not 23 divides 3329 by NAT_4:9; :: thesis:
3329 = (29 * 114) + 23 ;
hence not 29 divides 3329 by NAT_4:9; :: thesis:
3329 = (31 * 107) + 12 ;
hence not 31 divides 3329 by NAT_4:9; :: thesis:
3329 = (37 * 89) + 36 ;
hence not 37 divides 3329 by NAT_4:9; :: thesis:
3329 = (41 * 81) + 8 ;
hence not 41 divides 3329 by NAT_4:9; :: thesis:
3329 = (43 * 77) + 18 ;
hence not 43 divides 3329 by NAT_4:9; :: thesis:
3329 = (47 * 70) + 39 ;
hence not 47 divides 3329 by NAT_4:9; :: thesis:
3329 = (53 * 62) + 43 ;
hence not 53 divides 3329 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3329 & n is prime holds
not n divides 3329 by XPRIMET1:32;
hence 3329 is prime by NAT_4:14; :: thesis: