 In about 300 BC Euclid showed that if 2"p" − 1 is prime then 2"p"−1(2"p" − 1) is perfect.The first four perfect numbers were the only ones known to early Greek mathematics, and the mathematician Nicomachus noted 8128 as early as around AD 100.Nicomachus states without proof that every perfect number is (putting it in our terms) of the form formula_5 where formula_6 is prime.