
theorem
  521 is prime
proof
  now
    521 = 2*260 + 1; hence not 2 divides 521 by NAT_4:9;
    521 = 3*173 + 2; hence not 3 divides 521 by NAT_4:9;
    521 = 5*104 + 1; hence not 5 divides 521 by NAT_4:9;
    521 = 7*74 + 3; hence not 7 divides 521 by NAT_4:9;
    521 = 11*47 + 4; hence not 11 divides 521 by NAT_4:9;
    521 = 13*40 + 1; hence not 13 divides 521 by NAT_4:9;
    521 = 17*30 + 11; hence not 17 divides 521 by NAT_4:9;
    521 = 19*27 + 8; hence not 19 divides 521 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 521 & n is prime
  holds not n divides 521 by XPRIMET1:16;
  hence thesis by NAT_4:14;
