
theorem
  373 is prime
proof
  now
    373 = 2*186 + 1; hence not 2 divides 373 by NAT_4:9;
    373 = 3*124 + 1; hence not 3 divides 373 by NAT_4:9;
    373 = 5*74 + 3; hence not 5 divides 373 by NAT_4:9;
    373 = 7*53 + 2; hence not 7 divides 373 by NAT_4:9;
    373 = 11*33 + 10; hence not 11 divides 373 by NAT_4:9;
    373 = 13*28 + 9; hence not 13 divides 373 by NAT_4:9;
    373 = 17*21 + 16; hence not 17 divides 373 by NAT_4:9;
    373 = 19*19 + 12; hence not 19 divides 373 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 373 & n is prime
  holds not n divides 373 by XPRIMET1:16;
  hence thesis by NAT_4:14;
