**Infinitely many even perfect numbers conjecture.**
Are there infinitely many even perfect numbers?
This is equivalent to asking whether there are infinitely many Mersenne primes,
since by the Euclid–Euler theorem an even number is perfect if and only if it
has the form $2^{p-1}(2^p - 1)$ where $2^p - 1$ is a Mersenne prime.
*Reference:*
[Wikipedia](https://en.wikipedia.org/wiki/Perfect_number)
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