20190313, 11:41  #1 
"Rashid Naimi"
Oct 2015
Out of my Body
2^{3}×229 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 20190313 at 11:54 
20190314, 00:17  #3 
"Rashid Naimi"
Oct 2015
Out of my Body
2^{3}·229 Posts 
Thank you Kar_bon for the reference.
There doesn't seem to be any large scale collaborative effort for the types. 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 N1 (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. 
20190314, 00:44  #4 
"Rashid Naimi"
Oct 2015
Out of my Body
2^{3}×229 Posts 
The Largest Prime of the form that I have found so far with very little effort.
*** 17507*2*(2^2160911 )+1 *** CPS600A by Rashid Naimi ** 65055 dd ** a = 17 Proven prime using PFGW as well as my own PariGP code. Last fiddled with by a1call on 20190314 at 00:53 
20190314, 01:01  #5 
"Rashid Naimi"
Oct 2015
Out of my Body
2^{3}·229 Posts 
Seems to be a new prime:

20190314, 01:44  #6 
"Rashid Naimi"
Oct 2015
Out of my Body
3450_{8} Posts 
Some more primes of the form that had not been reported to factorDb prior to today:
1713*2*(2^99411)+1 291*6*(2^96891 )+1 873*2*(2^96891)+1 4689*6*(2^44231 )+1 335*6*(2^42531 )+1 
20190314, 01:48  #7 
"Rashid Naimi"
Oct 2015
Out of my Body
2^{3}·229 Posts 
and yet some more with very few digits which had not been reported to FactorDb prior to today:
2016*6*(2^32171 )+1 504*6*(2^12791 )+1 114*6*(2^6071 )+1 56*6*(2^891 )+1 
20190320, 05:25  #8 
"Rashid Naimi"
Oct 2015
Out of my Body
1832_{10} Posts 

20190320, 06:01  #9 
Jun 2003
121D_{16} 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))

20190320, 08:11  #10 
"Rashid Naimi"
Oct 2015
Out of my Body
728_{16} 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. 
20190320, 08:29  #11 
Jun 2003
4,637 Posts 
