
theorem
  607 is prime
proof
  now
    607 = 2*303 + 1; hence not 2 divides 607 by NAT_4:9;
    607 = 3*202 + 1; hence not 3 divides 607 by NAT_4:9;
    607 = 5*121 + 2; hence not 5 divides 607 by NAT_4:9;
    607 = 7*86 + 5; hence not 7 divides 607 by NAT_4:9;
    607 = 11*55 + 2; hence not 11 divides 607 by NAT_4:9;
    607 = 13*46 + 9; hence not 13 divides 607 by NAT_4:9;
    607 = 17*35 + 12; hence not 17 divides 607 by NAT_4:9;
    607 = 19*31 + 18; hence not 19 divides 607 by NAT_4:9;
    607 = 23*26 + 9; hence not 23 divides 607 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 607 & n is prime
  holds not n divides 607 by XPRIMET1:18;
  hence thesis by NAT_4:14;
