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Are there infinitely many perfect numbers?

Are there infinitely many perfect numbers?

Grade:upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
nobody knows whether or not there are infinitely many perfect numbers. As you have probably found out, all the even perfect numbers are of the form 2^(p-1) * (2^p - 1), where both p and 2^p - 1 are prime. Primes of the form 2^p - 1 are called Mersenne primes, and the largest known primes are Mersenne primes, but nobody knows whether there are an infinite number of them or not.It is also unknown whether or not there are any odd perfect numbers.
Thanks and Regards
Shaik Aasif
askIITians faculty

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