1103 = (2 * 551) + 1 ;
hence not 2 divides 1103 by NAT_4:9; :: thesis:
1103 = (3 * 367) + 2 ;
hence not 3 divides 1103 by NAT_4:9; :: thesis:
1103 = (5 * 220) + 3 ;
hence not 5 divides 1103 by NAT_4:9; :: thesis:
1103 = (7 * 157) + 4 ;
hence not 7 divides 1103 by NAT_4:9; :: thesis:
1103 = (11 * 100) + 3 ;
hence not 11 divides 1103 by NAT_4:9; :: thesis:
1103 = (13 * 84) + 11 ;
hence not 13 divides 1103 by NAT_4:9; :: thesis:
1103 = (17 * 64) + 15 ;
hence not 17 divides 1103 by NAT_4:9; :: thesis:
1103 = (19 * 58) + 1 ;
hence not 19 divides 1103 by NAT_4:9; :: thesis:
1103 = (23 * 47) + 22 ;
hence not 23 divides 1103 by NAT_4:9; :: thesis:
1103 = (29 * 38) + 1 ;
hence not 29 divides 1103 by NAT_4:9; :: thesis:
1103 = (31 * 35) + 18 ;
hence not 31 divides 1103 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1103 & n is prime holds
not n divides 1103 by XPRIMET1:22;
hence 1103 is prime by NAT_4:14; :: thesis: