
theorem
  599 is prime
proof
  now
    599 = 2*299 + 1; hence not 2 divides 599 by NAT_4:9;
    599 = 3*199 + 2; hence not 3 divides 599 by NAT_4:9;
    599 = 5*119 + 4; hence not 5 divides 599 by NAT_4:9;
    599 = 7*85 + 4; hence not 7 divides 599 by NAT_4:9;
    599 = 11*54 + 5; hence not 11 divides 599 by NAT_4:9;
    599 = 13*46 + 1; hence not 13 divides 599 by NAT_4:9;
    599 = 17*35 + 4; hence not 17 divides 599 by NAT_4:9;
    599 = 19*31 + 10; hence not 19 divides 599 by NAT_4:9;
    599 = 23*26 + 1; hence not 23 divides 599 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 599 & n is prime
  holds not n divides 599 by XPRIMET1:18;
  hence thesis by NAT_4:14;
