3299 = (2 * 1649) + 1 ;
hence not 2 divides 3299 by NAT_4:9; :: thesis:
3299 = (3 * 1099) + 2 ;
hence not 3 divides 3299 by NAT_4:9; :: thesis:
3299 = (5 * 659) + 4 ;
hence not 5 divides 3299 by NAT_4:9; :: thesis:
3299 = (7 * 471) + 2 ;
hence not 7 divides 3299 by NAT_4:9; :: thesis:
3299 = (11 * 299) + 10 ;
hence not 11 divides 3299 by NAT_4:9; :: thesis:
3299 = (13 * 253) + 10 ;
hence not 13 divides 3299 by NAT_4:9; :: thesis:
3299 = (17 * 194) + 1 ;
hence not 17 divides 3299 by NAT_4:9; :: thesis:
3299 = (19 * 173) + 12 ;
hence not 19 divides 3299 by NAT_4:9; :: thesis:
3299 = (23 * 143) + 10 ;
hence not 23 divides 3299 by NAT_4:9; :: thesis:
3299 = (29 * 113) + 22 ;
hence not 29 divides 3299 by NAT_4:9; :: thesis:
3299 = (31 * 106) + 13 ;
hence not 31 divides 3299 by NAT_4:9; :: thesis:
3299 = (37 * 89) + 6 ;
hence not 37 divides 3299 by NAT_4:9; :: thesis:
3299 = (41 * 80) + 19 ;
hence not 41 divides 3299 by NAT_4:9; :: thesis:
3299 = (43 * 76) + 31 ;
hence not 43 divides 3299 by NAT_4:9; :: thesis:
3299 = (47 * 70) + 9 ;
hence not 47 divides 3299 by NAT_4:9; :: thesis:
3299 = (53 * 62) + 13 ;
hence not 53 divides 3299 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3299 & n is prime holds
not n divides 3299 by XPRIMET1:32;
hence 3299 is prime by NAT_4:14; :: thesis: