
theorem
  337 is prime
proof
  now
    337 = 2*168 + 1; hence not 2 divides 337 by NAT_4:9;
    337 = 3*112 + 1; hence not 3 divides 337 by NAT_4:9;
    337 = 5*67 + 2; hence not 5 divides 337 by NAT_4:9;
    337 = 7*48 + 1; hence not 7 divides 337 by NAT_4:9;
    337 = 11*30 + 7; hence not 11 divides 337 by NAT_4:9;
    337 = 13*25 + 12; hence not 13 divides 337 by NAT_4:9;
    337 = 17*19 + 14; hence not 17 divides 337 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 337 & n is prime
  holds not n divides 337 by XPRIMET1:14;
  hence thesis by NAT_4:14;
