
theorem
  331 is prime
proof
  now
    331 = 2*165 + 1; hence not 2 divides 331 by NAT_4:9;
    331 = 3*110 + 1; hence not 3 divides 331 by NAT_4:9;
    331 = 5*66 + 1; hence not 5 divides 331 by NAT_4:9;
    331 = 7*47 + 2; hence not 7 divides 331 by NAT_4:9;
    331 = 11*30 + 1; hence not 11 divides 331 by NAT_4:9;
    331 = 13*25 + 6; hence not 13 divides 331 by NAT_4:9;
    331 = 17*19 + 8; hence not 17 divides 331 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 331 & n is prime
  holds not n divides 331 by XPRIMET1:14;
  hence thesis by NAT_4:14;
end;
