# Talk:Double Mersenne number

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At approximately what time will all Mersenne exponents below 80,000,000 checked for whether they are prime?? (This is just about how far http://mersenne.org/status.htm goes.) 66.245.19.60 22:02, 10 May 2004 (UTC)

This reference might help: http://www.utm.edu/research/primes/notes/faq/NextMersenne.html. Giftlite 23:56, 10 May 2004 (UTC)

## Just a Conjecture but...

I believe that $M_{M_{127}}$ , or 2170141183460469231731687303715884105727 - 1, is prime. At approximately 5.12176 × 1037 digits, it may be centuries before I am proven correct or incorrect. Also, I believe that this is the fifth, final, and largest Double Mersenne prime. In other words, I believe that $M_{M_{n}}$  is composite for all n > 7, expect for n = 127. PhiEaglesfan712 20:32, 12 July 2007 (UTC)

How about n = $M_{127}$ ???

I don’t think this number is prime, for another similar example of repeated exponents, 2+1=3 is prime, 2^2+1=5 is prime, 2^(2^2)+1=17 is prime, 2^(2^(2^2))+1=65537 is also prime, but 2^(2^(2^(2^2)))+1=2^65536+1 is not prime. For the original sequence, 2^2-1=3 is prime, 2^(2^2-1)-1=7 is prime, 2^(2^(2^2-1)-1)-1=127 is prime, 2^(2^(2^(2^2-1)-1)-1)-1 is also prime, but the next number 2^(2^(2^(2^2-1)-1)-1)-1 may not be prime. These two sequences are similar, and the first four terms of both sequences are all primes, but the fifth (and further) terms are (conjectured) all composite. 61.224.41.36 (talk) 09:46, 23 February 2019 (UTC)

## Changed definition

PhiEaglesfan712 has just changed the definition of double Mersenne number  and Mersenne number . I think both should be changed back. I suggest to keep comments together at Talk:Mersenne prime#Mersenne number. PrimeHunter 23:52, 14 August 2007 (UTC)

## Catalan-Mersenne numbers

I have a source in Slovene that Catalan-Mersenne numbers are also called "Cantor('s) numbers" (and I've made an article with this name - Cantorjevo število, since I've found this name in source), perhaps mainly because Georg Cantor allegedly conjectured that these kind of numbers are all primes. Does anybody perhaps have similar English source for this? --xJaM (talk) 00:55, 19 January 2011 (UTC)

## Double Wagstaff Numbers

Let $M_{n}$ =$2^{n}-1$ , $W_{n}$ =$(2^{n}+1)/3$ , we know that when n = 2, 3, 5, 7, then $M_{M_{n}}$  is a prime, but when n = 13, 17, 19, 31, it's not, and we know that when n = 2, 3, 5, 7, then $W_{W_{n}}$  is a prime, but when n = 11, 13, 17, 19, 23, 31, it's not. I believe that when n>7 (Except of n=43 and n=127), both $M_{M_{n}}$  and $W_{W_{n}}$  are not primes, but $W_{W_{43}}$  is a prime, and $M_{M_{127}}$  and $W_{W_{127}}$  are the largest double Mersenne prime and double Wagstaff prime.(Because 43 is $W_{7}$  and 127 is $M_{7}$ )