now :: thesis: ( not 2 divides 29 & not 3 divides 29 & not 5 divides 29 )

29 = (2 * 14) + 1 ;
hence not 2 divides 29 by NAT_4:9; :: thesis: ( not 3 divides 29 & not 5 divides 29 )
29 = (3 * 9) + 2 ;
hence not 3 divides 29 by NAT_4:9; :: thesis: not 5 divides 29
29 = (5 * 5) + 4 ;
hence not 5 divides 29 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 29 & n is prime holds
not n divides 29 by XPRIMET1:6;
hence 29 is prime by NAT_4:14; :: thesis: verum