
theorem
  461 is prime
proof
  now
    461 = 2*230 + 1; hence not 2 divides 461 by NAT_4:9;
    461 = 3*153 + 2; hence not 3 divides 461 by NAT_4:9;
    461 = 5*92 + 1; hence not 5 divides 461 by NAT_4:9;
    461 = 7*65 + 6; hence not 7 divides 461 by NAT_4:9;
    461 = 11*41 + 10; hence not 11 divides 461 by NAT_4:9;
    461 = 13*35 + 6; hence not 13 divides 461 by NAT_4:9;
    461 = 17*27 + 2; hence not 17 divides 461 by NAT_4:9;
    461 = 19*24 + 5; hence not 19 divides 461 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 461 & n is prime
  holds not n divides 461 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
