 In 1588, the Italian mathematician Pietro Cataldi identified the sixth (8,589,869,056) and the seventh (137,438,691,328) perfect numbers, and also proved that every perfect number obtained from Euclid's rule ends with a 6 or an 8.Euclid proved that 2"p"−1(2"p" − 1) is an even perfect number whenever 2"p" − 1 is prime (Elements, Prop.IX.36).