 In fact, Mersenne primes are very rare—of the 2,610,944 prime numbers "p" up to 43,112,609, 
2"p" − 1 is prime for only 47 of them.Although Nicomachus had stated (without proof) that all perfect numbers were of the form formula_5 where formula_6 is prime (though he stated this somewhat differently), Ibn al-Haytham (Alhazen) circa AD 1000 conjectured only that every even perfect number is of that form.It was not until the 18th century that Leonhard Euler proved that the formula 2"p"−1(2"p" − 1) will yield all the even perfect numbers.