3319 = (2 * 1659) + 1 ;
hence not 2 divides 3319 by NAT_4:9; :: thesis:
3319 = (3 * 1106) + 1 ;
hence not 3 divides 3319 by NAT_4:9; :: thesis:
3319 = (5 * 663) + 4 ;
hence not 5 divides 3319 by NAT_4:9; :: thesis:
3319 = (7 * 474) + 1 ;
hence not 7 divides 3319 by NAT_4:9; :: thesis:
3319 = (11 * 301) + 8 ;
hence not 11 divides 3319 by NAT_4:9; :: thesis:
3319 = (13 * 255) + 4 ;
hence not 13 divides 3319 by NAT_4:9; :: thesis:
3319 = (17 * 195) + 4 ;
hence not 17 divides 3319 by NAT_4:9; :: thesis:
3319 = (19 * 174) + 13 ;
hence not 19 divides 3319 by NAT_4:9; :: thesis:
3319 = (23 * 144) + 7 ;
hence not 23 divides 3319 by NAT_4:9; :: thesis:
3319 = (29 * 114) + 13 ;
hence not 29 divides 3319 by NAT_4:9; :: thesis:
3319 = (31 * 107) + 2 ;
hence not 31 divides 3319 by NAT_4:9; :: thesis:
3319 = (37 * 89) + 26 ;
hence not 37 divides 3319 by NAT_4:9; :: thesis:
3319 = (41 * 80) + 39 ;
hence not 41 divides 3319 by NAT_4:9; :: thesis:
3319 = (43 * 77) + 8 ;
hence not 43 divides 3319 by NAT_4:9; :: thesis:
3319 = (47 * 70) + 29 ;
hence not 47 divides 3319 by NAT_4:9; :: thesis:
3319 = (53 * 62) + 33 ;
hence not 53 divides 3319 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3319 & n is prime holds
not n divides 3319 by XPRIMET1:32;
hence 3319 is prime by NAT_4:14; :: thesis: