now :: thesis: ( not 2 divides 103 & not 3 divides 103 & not 5 divides 103 & not 7 divides 103 )

103 = (2 * 51) + 1 ;
hence not 2 divides 103 by NAT_4:9; :: thesis: ( not 3 divides 103 & not 5 divides 103 & not 7 divides 103 )
103 = (3 * 34) + 1 ;
hence not 3 divides 103 by NAT_4:9; :: thesis: ( not 5 divides 103 & not 7 divides 103 )
103 = (5 * 20) + 3 ;
hence not 5 divides 103 by NAT_4:9; :: thesis: not 7 divides 103
103 = (7 * 14) + 5 ;
hence not 7 divides 103 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 103 & n is prime holds
not n divides 103 by XPRIMET1:8;
hence 103 is prime by NAT_4:14; :: thesis: verum