Reference material discussion thread

[axn]

Originally Posted by kriesel

Added to https://www.mersenneforum.org/showpo...9&postcount=29.

Thanks. It looks like it is doing the right thing and should be, in theory, little bit (10-15%) faster than v6 stage 2.

I believe you said there was a general FFT regression from v6 to v7. Could this explain why v7 stage 2 is slower than v6, despite having a better stage 2 algorithm?

[kriesel]

Originally Posted by axn

I believe you said there was a general FFT regression from v6 to v7.

It depends on the fft length apparently, per https://www.mersenneforum.org/showpo...35&postcount=2

Note due to the time required for even a single PRP benchmark per fft length across all supported lengths per selected Gpuowl version and single OS version, the tabulated values are single measurements each

Could this explain why v7 stage 2 is slower than v6, despite having a better stage 2 algorithm?

Partially. It does not explain the full magnitude of discrepancy in V7/v6 P-1 performance ratio, between ~112% expectation and ~75% observation.

[kriesel]

In https://mathworld.wolfram.com/PrimeFormulas.html there is a constant 1.92878218715...
Does it have a name? Wright's constant? A web search for "Wright's constant" came up apparently void of relevant hits.

[Dr Sardonicus]

Originally Posted by kriesel

In https://mathworld.wolfram.com/PrimeFormulas.html there is a constant 1.92878218715...
Does it have a name? Wright's constant? A web search for "Wright's constant" came up apparently void of relevant hits.

The blog post Prime generating functions and the Buenos Aires constant has the passage

There are also functions generating primes from constants that are defined using all primes (actually, in Mills’ and Wright’s constants the same thing happens, it’s just that it is more hidden through an exists, and now there is going to be an explicit formula for the constant).

which refers to the constant in question as "Wright's constant."

As to the "Buenos Aires constant" itself, see this thread and this thread.

[kriesel]

Originally Posted by Dr Sardonicus

The blog post Prime generating functions and the Buenos Aires constant has the passage which refers to the constant in question as "Wright's constant."

As to the "Buenos Aires constant" itself, see this thread and this thread.

Thank you. This page has been updated with the Wright's constant name and a graph of the listed constants.

[jwaltos]

Wow! Your resource thread is a great thread!
A quick question, without recourse to sieving (Eratosthenes..etc) is there a formulaic rather than mechanistic method of testing if a number is prime or not?
That is, is there a one-shot, single try expression with a pass/fail result rather than an automated, time dependent process? I'm assuming there isn't and I don't know if the AKS test is a step in such a direction.

[kriesel]

Originally Posted by jwaltos

without recourse to sieving, is there a primality test that you're aware of?

I'm focused here on Mersennes. The standard is Lucas-Lehmer. If you're asking about general primes, I'm not the guy to ask.


(edit) This blog is intended to be a focused reference resource for GIMPS computing mostly GPU oriented. Not for general number theory; there are threads and subfora for that.

[slandrum]

Originally Posted by jwaltos

A quick question, without recourse to sieving (Eratosthenes..etc) is there a formulaic rather than mechanistic method of testing if a number is prime or not?
That is, is there a one-shot, single try expression with a pass/fail result rather than an automated, time dependent process? I'm assuming there isn't and I don't know if the AKS test is a step in such a direction.

Well, a simple expression that will give you the answer is GCD(n, floor(n^(1/2))!) - but computing that answer is something else entirely.

[DrobinsonPE]

Ken, in reference to this post, https://www.mersenneforum.org/showpo...4&postcount=10

Please try using -lgc instead of -pl

I have a GTX 1650 super. Initially I was using -pl to explore the energy efficiency of the card just as you have. nvidia-smi only allowed me to adjust the range between 70-100w and like you discovered, the most energy efficient setting was 70W.

When I used -lgc, I was able to lower the power use significantly below 70w and discovered that the most energy efficient setting was -lgc 1300. See the attached picture.