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January 3

50th perfect number

How many digits (I want an exact figure) does the 50th perfect number have?? I know it falls between 46 million and 47 million, but I want an exact figure. Georgia guy (talk) 18:29, 3 January 2018 (UTC)[reply]

According to [1], the recently discovered Mersenne prime is 2^77232917-1. This means that the corresponding perfect number is 2^77232916(2^77232917-1). According to my calculations the logarithm is 46498849.03822324341502, so it has 46498850 digits and starts with 1092... . It should be noted this is the 50th known Mersenne prime, not necessarily the 50th is size, as the the search method is not guaranteed to find the primes in order. --RDBury (talk) 18:59, 3 January 2018 (UTC)[reply]

Right. I updated List of perfect numbers. PrimeHunter (talk) 02:56, 6 January 2018 (UTC)[reply]

I'm not into math much, but a Perfect number is not the same as a prime number is it? RudolfRed (talk) 19:51, 3 January 2018 (UTC)[reply]

No but every perfect number is associated with a Mersenne prime and vice versa. See Euclid-Euler theorem. CodeTalker (talk) 20:21, 3 January 2018 (UTC)[reply]

Technically, what's been proved is that that's true for every even perfect number. Almost certainly, there are no odd perfect numbers, but this has not been proved. --Trovatore (talk) 20:31, 3 January 2018 (UTC)[reply]

For more context, see Mersenne prime, especially the 3 January announcement of a newly discovered one. Double sharp (talk) 10:15, 5 January 2018 (UTC)[reply]

A question of Topology by Munkres

Give an example of a function that has a left inverse but no right inverse.
Give an example of a function that has a right inverse but no left inverse.
Can a function have more than one left inverse? more than one right inverse?

Thanks in advance. Alireza Badali (talk) 20:34, 3 January 2018 (UTC)[reply]

Have you read Inverse function#Left and right inverses? -- ToE 22:07, 3 January 2018 (UTC)[reply]

Thank you, no I hadn't seen it, so Wikipedia has everything, thanks to Wikipedia too! Alireza Badali (talk) 08:30, 4 January 2018 (UTC)[reply]