
theorem
  601 is prime
proof
  now
    601 = 2*300 + 1; hence not 2 divides 601 by NAT_4:9;
    601 = 3*200 + 1; hence not 3 divides 601 by NAT_4:9;
    601 = 5*120 + 1; hence not 5 divides 601 by NAT_4:9;
    601 = 7*85 + 6; hence not 7 divides 601 by NAT_4:9;
    601 = 11*54 + 7; hence not 11 divides 601 by NAT_4:9;
    601 = 13*46 + 3; hence not 13 divides 601 by NAT_4:9;
    601 = 17*35 + 6; hence not 17 divides 601 by NAT_4:9;
    601 = 19*31 + 12; hence not 19 divides 601 by NAT_4:9;
    601 = 23*26 + 3; hence not 23 divides 601 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 601 & n is prime
  holds not n divides 601 by XPRIMET1:18;
  hence thesis by NAT_4:14;
