
theorem
  523 is prime
proof
  now
    523 = 2*261 + 1; hence not 2 divides 523 by NAT_4:9;
    523 = 3*174 + 1; hence not 3 divides 523 by NAT_4:9;
    523 = 5*104 + 3; hence not 5 divides 523 by NAT_4:9;
    523 = 7*74 + 5; hence not 7 divides 523 by NAT_4:9;
    523 = 11*47 + 6; hence not 11 divides 523 by NAT_4:9;
    523 = 13*40 + 3; hence not 13 divides 523 by NAT_4:9;
    523 = 17*30 + 13; hence not 17 divides 523 by NAT_4:9;
    523 = 19*27 + 10; hence not 19 divides 523 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 523 & n is prime
  holds not n divides 523 by XPRIMET1:16;
  hence thesis by NAT_4:14;
