
theorem
  179 is prime
proof
  now
    179 = 2*89 + 1; hence not 2 divides 179 by NAT_4:9;
    179 = 3*59 + 2; hence not 3 divides 179 by NAT_4:9;
    179 = 5*35 + 4; hence not 5 divides 179 by NAT_4:9;
    179 = 7*25 + 4; hence not 7 divides 179 by NAT_4:9;
    179 = 11*16 + 3; hence not 11 divides 179 by NAT_4:9;
    179 = 13*13 + 10; hence not 13 divides 179 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 179 & n is prime
  holds not n divides 179 by XPRIMET1:12;
  hence thesis by NAT_4:14;
end;
