1433 = (2 * 716) + 1 ;
hence not 2 divides 1433 by NAT_4:9; :: thesis:
1433 = (3 * 477) + 2 ;
hence not 3 divides 1433 by NAT_4:9; :: thesis:
1433 = (5 * 286) + 3 ;
hence not 5 divides 1433 by NAT_4:9; :: thesis:
1433 = (7 * 204) + 5 ;
hence not 7 divides 1433 by NAT_4:9; :: thesis:
1433 = (11 * 130) + 3 ;
hence not 11 divides 1433 by NAT_4:9; :: thesis:
1433 = (13 * 110) + 3 ;
hence not 13 divides 1433 by NAT_4:9; :: thesis:
1433 = (17 * 84) + 5 ;
hence not 17 divides 1433 by NAT_4:9; :: thesis:
1433 = (19 * 75) + 8 ;
hence not 19 divides 1433 by NAT_4:9; :: thesis:
1433 = (23 * 62) + 7 ;
hence not 23 divides 1433 by NAT_4:9; :: thesis:
1433 = (29 * 49) + 12 ;
hence not 29 divides 1433 by NAT_4:9; :: thesis:
1433 = (31 * 46) + 7 ;
hence not 31 divides 1433 by NAT_4:9; :: thesis:
1433 = (37 * 38) + 27 ;
hence not 37 divides 1433 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1433 & n is prime holds
not n divides 1433 by XPRIMET1:24;
hence 1433 is prime by NAT_4:14; :: thesis: