1399 = (2 * 699) + 1 ;
hence not 2 divides 1399 by NAT_4:9; :: thesis:
1399 = (3 * 466) + 1 ;
hence not 3 divides 1399 by NAT_4:9; :: thesis:
1399 = (5 * 279) + 4 ;
hence not 5 divides 1399 by NAT_4:9; :: thesis:
1399 = (7 * 199) + 6 ;
hence not 7 divides 1399 by NAT_4:9; :: thesis:
1399 = (11 * 127) + 2 ;
hence not 11 divides 1399 by NAT_4:9; :: thesis:
1399 = (13 * 107) + 8 ;
hence not 13 divides 1399 by NAT_4:9; :: thesis:
1399 = (17 * 82) + 5 ;
hence not 17 divides 1399 by NAT_4:9; :: thesis:
1399 = (19 * 73) + 12 ;
hence not 19 divides 1399 by NAT_4:9; :: thesis:
1399 = (23 * 60) + 19 ;
hence not 23 divides 1399 by NAT_4:9; :: thesis:
1399 = (29 * 48) + 7 ;
hence not 29 divides 1399 by NAT_4:9; :: thesis:
1399 = (31 * 45) + 4 ;
hence not 31 divides 1399 by NAT_4:9; :: thesis:
1399 = (37 * 37) + 30 ;
hence not 37 divides 1399 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1399 & n is prime holds
not n divides 1399 by XPRIMET1:24;
hence 1399 is prime by NAT_4:14; :: thesis: