
theorem
  383 is prime
proof
  now
    383 = 2*191 + 1; hence not 2 divides 383 by NAT_4:9;
    383 = 3*127 + 2; hence not 3 divides 383 by NAT_4:9;
    383 = 5*76 + 3; hence not 5 divides 383 by NAT_4:9;
    383 = 7*54 + 5; hence not 7 divides 383 by NAT_4:9;
    383 = 11*34 + 9; hence not 11 divides 383 by NAT_4:9;
    383 = 13*29 + 6; hence not 13 divides 383 by NAT_4:9;
    383 = 17*22 + 9; hence not 17 divides 383 by NAT_4:9;
    383 = 19*20 + 3; hence not 19 divides 383 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 383 & n is prime
  holds not n divides 383 by XPRIMET1:16;
  hence thesis by NAT_4:14;
