New Subprojects

Cruelty · 2007-07-10, 15:04

The real question as I would imagine is: can someone post primes that do not fit into one of the three subprojects defined on RPS project page?
Another, similar question: can we extend the list of subprojects?
Some candidates that come to my mind include:
- Gaussian Mersenne Norms and co-norms (PRPs)
- high-weight "k" proth primes (as suggested by Roger)
- some other ideas developed by participating individuals (e.g. I am working right now on primes of the form "4*3^n-1")

Kosmaj · 2007-07-21, 13:34

I think we can indeed extend the list of sub-projects to include Gaussian Mersenne Norms and co-norms and Sophie-Germain primes when p=k*2^n-1 (but excluding p=k*2^n+1) where p is the smaller prime of the Sophie Germain pair.

I'd like to suggest that we resist the temptation of adding high weight Proth primes, k*2^n+1, because one has to stop somewhere

Of course everybody is free to pursue other side-projects unrelated to RPS. Specifically, for high weight Proth primes there is a project started by Robert and Phil Carmody where I took part for a while but currently it has no primes in the Top-5000

As for 4*3^n-1 note that prof. Iskra (whom I think you already "met") developed his own method but I think it works only for 4*3^n+1 and he already reported tens of primes of that form.

Kosmaj · 2007-07-22, 10:03

I just created a new thread to discuss new subprojects.

If you agree I'd like to suggest that you lead the GM/GQ efforts.

Can you tell us for the beginning the status of the search, and what software is required to search for such primes/PRPs. I beleive LLR alone is enough but it has to be one of the latest versions. Is that right?

Info on some illustrative exe times will be appreciated as well.

Cruelty · 2012-08-30, 21:58

k=2 and k=4 @ base=3 tested till n=1.13M
112*113^n-1 tested till n=240k (looking for the first Williams prime for this base)

Cruelty · 2012-09-30, 12:40

k=2 and k=4 @ base=3 tested till n=1.14M
112*113^n-1 tested till n=280k

Cruelty · 2012-10-02, 21:14

I release 112*113ⁿ-1 @ n=290k.

Cruelty · 2012-11-01, 00:09

k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n-1 tested till n=4M

Cruelty · 2012-12-01, 17:57

k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n-1 tested till n=4.05M

Cruelty · 2012-12-03, 13:55

Quote:

Originally Posted by Cruelty

k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n-1 tested till n=4.05M

My mistake: should be 127*128^n-1 tested till n=580k

Cruelty · 2013-01-31, 10:46

k=2 and k=4 @ base=3 tested till n=1.17M
127*128^n-1 tested till n=620k

Cruelty · 2013-03-02, 01:26

k=2 and k=4 @ base=3 tested till n=1.17M
127*128^n-1 tested till n=640k

2007-07-10, 15:04	#1
Cruelty May 2005 65C₁₆ Posts	New Subprojects The real question as I would imagine is: can someone post primes that do not fit into one of the three subprojects defined on RPS project page? Another, similar question: can we extend the list of subprojects? Some candidates that come to my mind include: - Gaussian Mersenne Norms and co-norms (PRPs) - high-weight "k" proth primes (as suggested by Roger) - some other ideas developed by participating individuals (e.g. I am working right now on primes of the form "4*3^n-1")

2007-07-22, 10:03	#3
Kosmaj Nov 2003 3622₁₀ Posts	Cruelty I just created a new thread to discuss new subprojects. If you agree I'd like to suggest that you lead the GM/GQ efforts. Can you tell us for the beginning the status of the search, and what software is required to search for such primes/PRPs. I beleive LLR alone is enough but it has to be one of the latest versions. Is that right? Info on some illustrative exe times will be appreciated as well.

2012-08-30, 21:58	#4
Cruelty May 2005 2²·11·37 Posts	status report k=2 and k=4 @ base=3 tested till n=1.13M 112*113^n-1 tested till n=240k (looking for the first Williams prime for this base)

2012-10-02, 21:14	#6
Cruelty May 2005 11001011100₂ Posts	Status report I release 112*113ⁿ-1 @ n=290k.

2012-11-01, 00:09	#7
Cruelty May 2005 2²·11·37 Posts	status report k=2 and k=4 @ base=3 tested till n=1.15M 127*128^n-1 tested till n=4M

2007-07-21, 13:34	#2
Kosmaj Nov 2003 3622₁₀ Posts	I think we can indeed extend the list of sub-projects to include Gaussian Mersenne Norms and co-norms and Sophie-Germain primes when p=k2^n-1 (but excluding p=k2^n+1) where p is the smaller prime of the Sophie Germain pair. I'd like to suggest that we resist the temptation of adding high weight Proth primes, k2^n+1, because one has to stop somewhere Of course everybody is free to pursue other side-projects unrelated to RPS. Specifically, for high weight Proth primes there is a project started by Robert and Phil Carmody where I took part for a while but currently it has no primes in the Top-5000 As for 43^n-1 note that prof. Iskra (whom I think you already "met") developed his own method but I think it works only for 4*3^n+1 and he already reported tens of primes of that form.

2012-09-30, 12:40	#5
Cruelty May 2005 2²·11·37 Posts	k=2 and k=4 @ base=3 tested till n=1.14M 112*113^n-1 tested till n=280k

2012-12-01, 17:57	#8
Cruelty May 2005 2²·11·37 Posts	k=2 and k=4 @ base=3 tested till n=1.15M 127*128^n-1 tested till n=4.05M

2013-01-31, 10:46	#10
Cruelty May 2005 2²×11×37 Posts	status report k=2 and k=4 @ base=3 tested till n=1.17M 127*128^n-1 tested till n=620k

2013-03-02, 01:26	#11
Cruelty May 2005 1628₁₀ Posts	status report k=2 and k=4 @ base=3 tested till n=1.17M 127*128^n-1 tested till n=640k