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 July 1st, 2016, 02:05 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 385 Thanks: 27 Math Focus: Number theory 8th perfect number and 9th Mersenne prime In the Wiki list of OEIS sequences, both the 8th perfect number and 9th Mersenne prime agree for their first 9 digits, but essentially not the rest. Is this anomaly mathematically explainable? Please see https://en.wikipedia.org/wiki/List_of_OEIS_sequences Last edited by Loren; July 1st, 2016 at 02:07 PM.
 July 1st, 2016, 03:29 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 688 Thanks: 243 I don't think there's any special reason. These sequences just happen to pass close to each other at those points.
 July 1st, 2016, 10:03 PM #3 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 385 Thanks: 27 Math Focus: Number theory That the initial two sequential strings agree approaches a billion to one: 2305843008139952128 8th Perfect 2305843009213693951 9th Mersenne Although Euclid showed them to be related, I would say very few perfect numbers and Mersenne primes have identical strings for the first half of their finite numbers. Last edited by Loren; July 1st, 2016 at 10:13 PM.
 July 18th, 2016, 11:57 AM #4 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Loren wrote ... "I would say very few perfect numbers and Mersenne primes have identical strings for the first half of their finite numbers." it's easy enough to see the first pair that satisfies your conjecture 8128 (4th Perfect Number) 8191 (5th Mersenne Prime) , $2^{13} - 1$ , $13= 2^{4} - 3$ You have the 8th perfect number connected to the 9th Mersenne Prime 9th Mersenne Prime is $2^{61} - 1$ , $61= 2^{6} - 3$ I used the two entries $2^{4} - 3$ , $2^{6} - 3$ and fooled around looking for a pattern by comparing a list of Mersenne Primes to a list of Perfect Numbers but got nowhere. Maybe someone else will have luck
 March 21st, 2017, 02:26 PM #5 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 385 Thanks: 27 Math Focus: Number theory Is this a mistake in the OEIS, or a fantastic coincidence? From the top...
 March 21st, 2017, 02:48 PM #6 Newbie   Joined: Mar 2017 From: Somewhere Posts: 1 Thanks: 0 what is a Mersenne Prime?
 March 21st, 2017, 02:53 PM #7 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 385 Thanks: 27 Math Focus: Number theory In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number that can be written in the form M(n) = 2^n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.
March 22nd, 2017, 02:06 AM   #8
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Quote:
 Originally Posted by Loren Is this a mistake in the OEIS, or a fantastic coincidence? From the top...
My feeling is that this is not a coincidence , there is underlying structure here waiting to be discovered. Mersenne Primes and perfect numbers are rigidly connected. Unfortunately I don't have the resources to investigate. Hope someone else does

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