
theorem
  431 is prime
proof
  now
    431 = 2*215 + 1; hence not 2 divides 431 by NAT_4:9;
    431 = 3*143 + 2; hence not 3 divides 431 by NAT_4:9;
    431 = 5*86 + 1; hence not 5 divides 431 by NAT_4:9;
    431 = 7*61 + 4; hence not 7 divides 431 by NAT_4:9;
    431 = 11*39 + 2; hence not 11 divides 431 by NAT_4:9;
    431 = 13*33 + 2; hence not 13 divides 431 by NAT_4:9;
    431 = 17*25 + 6; hence not 17 divides 431 by NAT_4:9;
    431 = 19*22 + 13; hence not 19 divides 431 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 431 & n is prime
  holds not n divides 431 by XPRIMET1:16;
  hence thesis by NAT_4:14;
