
theorem
  61 is prime
proof
  now
    61 = 2*30 + 1; hence not 2 divides 61 by NAT_4:9;
    61 = 3*20 + 1; hence not 3 divides 61 by NAT_4:9;
    61 = 5*12 + 1; hence not 5 divides 61 by NAT_4:9;
    61 = 7*8 + 5; hence not 7 divides 61 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 61 & n is prime
  holds not n divides 61 by XPRIMET1:8;
  hence thesis by NAT_4:14;
end;
