
theorem
  631 is prime
proof
  now
    631 = 2*315 + 1; hence not 2 divides 631 by NAT_4:9;
    631 = 3*210 + 1; hence not 3 divides 631 by NAT_4:9;
    631 = 5*126 + 1; hence not 5 divides 631 by NAT_4:9;
    631 = 7*90 + 1; hence not 7 divides 631 by NAT_4:9;
    631 = 11*57 + 4; hence not 11 divides 631 by NAT_4:9;
    631 = 13*48 + 7; hence not 13 divides 631 by NAT_4:9;
    631 = 17*37 + 2; hence not 17 divides 631 by NAT_4:9;
    631 = 19*33 + 4; hence not 19 divides 631 by NAT_4:9;
    631 = 23*27 + 10; hence not 23 divides 631 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 631 & n is prime
  holds not n divides 631 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
