
theorem
  83 is prime
proof
  now
    83 = 2*41 + 1; hence not 2 divides 83 by NAT_4:9;
    83 = 3*27 + 2; hence not 3 divides 83 by NAT_4:9;
    83 = 5*16 + 3; hence not 5 divides 83 by NAT_4:9;
    83 = 7*11 + 6; hence not 7 divides 83 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 83 & n is prime
  holds not n divides 83 by XPRIMET1:8;
  hence thesis by NAT_4:14;
end;
