
theorem
  307 is prime
proof
  now
    307 = 2*153 + 1; hence not 2 divides 307 by NAT_4:9;
    307 = 3*102 + 1; hence not 3 divides 307 by NAT_4:9;
    307 = 5*61 + 2; hence not 5 divides 307 by NAT_4:9;
    307 = 7*43 + 6; hence not 7 divides 307 by NAT_4:9;
    307 = 11*27 + 10; hence not 11 divides 307 by NAT_4:9;
    307 = 13*23 + 8; hence not 13 divides 307 by NAT_4:9;
    307 = 17*18 + 1; hence not 17 divides 307 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 307 & n is prime
  holds not n divides 307 by XPRIMET1:14;
  hence thesis by NAT_4:14;
end;
