
theorem
  593 is prime
proof
  now
    593 = 2*296 + 1; hence not 2 divides 593 by NAT_4:9;
    593 = 3*197 + 2; hence not 3 divides 593 by NAT_4:9;
    593 = 5*118 + 3; hence not 5 divides 593 by NAT_4:9;
    593 = 7*84 + 5; hence not 7 divides 593 by NAT_4:9;
    593 = 11*53 + 10; hence not 11 divides 593 by NAT_4:9;
    593 = 13*45 + 8; hence not 13 divides 593 by NAT_4:9;
    593 = 17*34 + 15; hence not 17 divides 593 by NAT_4:9;
    593 = 19*31 + 4; hence not 19 divides 593 by NAT_4:9;
    593 = 23*25 + 18; hence not 23 divides 593 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 593 & n is prime
  holds not n divides 593 by XPRIMET1:18;
  hence thesis by NAT_4:14;
