now :: thesis: ( not 2 divides 73 & not 3 divides 73 & not 5 divides 73 & not 7 divides 73 )

73 = (2 * 36) + 1 ;
hence not 2 divides 73 by NAT_4:9; :: thesis: ( not 3 divides 73 & not 5 divides 73 & not 7 divides 73 )
73 = (3 * 24) + 1 ;
hence not 3 divides 73 by NAT_4:9; :: thesis: ( not 5 divides 73 & not 7 divides 73 )
73 = (5 * 14) + 3 ;
hence not 5 divides 73 by NAT_4:9; :: thesis: not 7 divides 73
73 = (7 * 10) + 3 ;
hence not 7 divides 73 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 73 & n is prime holds
not n divides 73 by XPRIMET1:8;
hence 73 is prime by NAT_4:14; :: thesis: verum