mersenneforum.org k.Mp +/- 1
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 2019-03-13, 11:41 #1 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 1000110101102 Posts k.Mp +/- 1 Hi all, https://primes.utm.edu/primes/page.php?id=98189 What are primes of this form called? Are there any collaborative efforts at discovering primes oh this form? Thanks in advance. ETA Just realized that the thread title and the example don't match. I am interested to find out about both formats. Thanks again. Last fiddled with by a1call on 2019-03-13 at 11:54
 2019-03-13, 12:17 #2 kar_bon     Mar 2006 Germany B9016 Posts In an old 15k Search thread they're called 'General Mersenne primes" (as in Top5000 "Generalized Woodall/Cullen/Fermat") but not officially accepted.
 2019-03-14, 00:17 #3 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 1000110101102 Posts Thank you Kar_bon for the reference. There doesn't seem to be any large scale collaborative effort for the type-s. What I find surprising is that there seem to be no prime of the form k.Mp +/- 1 in the top 5k primes. the closest match seems to be : https://primes.utm.edu/primes/page.php?id=118696 It is surprising because at lower 100k dd they would take minuets to prove prime using N-1 (not sure about N+1). I also think they should not be too difficult to find. I have no 100k dd+ ones to back that up, but plenty of lower ones.
 2019-03-14, 00:44 #4 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×3×13×29 Posts The Largest Prime of the form that I have found so far with very little effort. *** 17507*2*(2^216091-1 )+1 *** CPS-600-A by Rashid Naimi ** 65055 dd ** a = 17 Proven prime using PFGW as well as my own Pari-GP code. Last fiddled with by a1call on 2019-03-14 at 00:53
 2019-03-14, 01:01 #5 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·3·13·29 Posts Seems to be a new prime: Attached Thumbnails
 2019-03-14, 01:44 #6 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×3×13×29 Posts Some more primes of the form that had not been reported to factorDb prior to today: 1713*2*(2^9941-1)+1 291*6*(2^9689-1 )+1 873*2*(2^9689-1)+1 4689*6*(2^4423-1 )+1 335*6*(2^4253-1 )+1 Attached Thumbnails
 2019-03-14, 01:48 #7 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·3·13·29 Posts and yet some more with very few digits which had not been reported to FactorDb prior to today: 2016*6*(2^3217-1 )+1 504*6*(2^1279-1 )+1 114*6*(2^607-1 )+1 56*6*(2^89-1 )+1 Attached Thumbnails
 2019-03-20, 05:25 #8 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·3·13·29 Posts Factordb finished N-1 test: http://factordb.com/index.php?query=...1%29*35014%2B1
 2019-03-20, 06:01 #9 axn     Jun 2003 33·199 Posts Look at the sub forum Operazione Doppi Mersennes which look for factors of double mersenne numbers. They are not interested in _all_ primes of the form k.Mp+1, but only those that can divide M(Mp) (hence 1 or 7 (mod 8))
 2019-03-20, 08:11 #10 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×3×13×29 Posts Well, that leaves more quickly proven primes for the rest of us. Compare proving a 65k dd prime in less a minute, to months (or is it years) required for a general prime of the same size. The whole point of this thread is to wonder why no top 5k primes of the type exist when they are much less time consuming than many of them that do. Thank you for the pointer though.
2019-03-20, 08:29   #11
axn

Jun 2003

33·199 Posts

Quote:
 Originally Posted by a1call The whole point of this thread is to wonder why no top 5k primes of the type exist when they are much less time consuming than many of them that do.
The form k*2^n+/-1 is even easier, hence the bulk of Top 5000 consists of these numbers.

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