
theorem
  769 is prime
proof
  now
    769 = 2*384 + 1; hence not 2 divides 769 by NAT_4:9;
    769 = 3*256 + 1; hence not 3 divides 769 by NAT_4:9;
    769 = 5*153 + 4; hence not 5 divides 769 by NAT_4:9;
    769 = 7*109 + 6; hence not 7 divides 769 by NAT_4:9;
    769 = 11*69 + 10; hence not 11 divides 769 by NAT_4:9;
    769 = 13*59 + 2; hence not 13 divides 769 by NAT_4:9;
    769 = 17*45 + 4; hence not 17 divides 769 by NAT_4:9;
    769 = 19*40 + 9; hence not 19 divides 769 by NAT_4:9;
    769 = 23*33 + 10; hence not 23 divides 769 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 769 & n is prime
  holds not n divides 769 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
