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Old 2020-11-13, 04:09   #4
swishzzz
 
Jan 2012
Toronto, Canada

1101102 Posts
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It has already been proven that an even number N is a perfect number if and only if N = 2^(k-1)*(2^k-1) and 2^k-1 is prime: https://primes.utm.edu/notes/proofs/EvenPerfect.html

As retina has mentioned, there has been much effort dedicated to finding odd perfect numbers and it has been shown that no such odd number exists below 10^1500 (and in all honesty is unlikely to exist). Current efforts there are focused on factoring "roadblock" numbers that can be many hundreds of digits long and even the smallest ones take months to years for a single machine to factor. We have a thread for that too: https://mersenneforum.org/showthread.php?t=19066
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