
theorem
  709 is prime
proof
  now
    709 = 2*354 + 1; hence not 2 divides 709 by NAT_4:9;
    709 = 3*236 + 1; hence not 3 divides 709 by NAT_4:9;
    709 = 5*141 + 4; hence not 5 divides 709 by NAT_4:9;
    709 = 7*101 + 2; hence not 7 divides 709 by NAT_4:9;
    709 = 11*64 + 5; hence not 11 divides 709 by NAT_4:9;
    709 = 13*54 + 7; hence not 13 divides 709 by NAT_4:9;
    709 = 17*41 + 12; hence not 17 divides 709 by NAT_4:9;
    709 = 19*37 + 6; hence not 19 divides 709 by NAT_4:9;
    709 = 23*30 + 19; hence not 23 divides 709 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 709 & n is prime
  holds not n divides 709 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
