k.Mp +/- 1

[a1call]

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.

[kar_bon]

In an old 15k Search thread they're called 'General Mersenne primes" (as in Top5000 "Generalized Woodall/Cullen/Fermat") but not officially accepted.

[a1call]

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.

[a1call]

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.

[a1call]

Seems to be a new prime:

[a1call]

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

[a1call]

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

[a1call]

Factordb finished N-1 test:
http://factordb.com/index.php?query=...1%29*35014%2B1

[axn]

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))

[a1call]

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.

[axn]

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.