
theorem
  59 is prime
proof
  now
    59 = 2*29 + 1; hence not 2 divides 59 by NAT_4:9;
    59 = 3*19 + 2; hence not 3 divides 59 by NAT_4:9;
    59 = 5*11 + 4; hence not 5 divides 59 by NAT_4:9;
    59 = 7*8 + 3; hence not 7 divides 59 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 59 & n is prime
  holds not n divides 59 by XPRIMET1:8;
  hence thesis by NAT_4:14;
end;
