OEIS - A057732 : 2^n + 3

[R.D. Silverman]

Originally Posted by danaj

That sounds very useful. Heck, I want that so I can play around with other tests. Edit referencing RDS comment: useful to people implementing these things for running on computers. It would offer little in terms of math other than speed up simple checks.

So why is it in a sub-forum for discussion of mathematics????

[Batalov]

Originally Posted by paulunderwood

Maybe if somebody could implement this with a simple GWNUM command line program and post the source, it might be useful and instructive to the community

Here it is!
Create a.abc file:

ABC $a*$b^$c$d
1 2 1321355 3

Start llr -d a.abc
and you will find that all-complex FFT is used which is better than generic. Nothing needs to be implemented.

Starting probable prime test of 2^1000020+3
Using all-complex AVX FFT length 64K, Pass1=256, Pass2=256, a = 3
...
2^1000020+3, bit: 250000 / 1000021 [24.99%].  Time per bit: 0.364 ms.

Even if you'd implement the LLT, it would add nothing to that. Speed would be the same and it would still be a PRP.

[paulunderwood]

Originally Posted by Batalov

Here it is!
Create a.abc file:

ABC $a*$b^$c$d
1 2 1321355 3

Start llr -d a.abc
and you will find that all-complex FFT is used which is better than generic. Nothing needs to be implemented.

Starting probable prime test of 2^1000020+3
Using all-complex AVX FFT length 64K, Pass1=256, Pass2=256, a = 3
...
2^1000020+3, bit: 250000 / 1000021 [24.99%].  Time per bit: 0.364 ms.

Even if you'd implement the LLT, it would add nothing to that. Speed would be the same and it would still be a PRP.

Here is what I meant:

• include GWNUM
• read some parameter(s) from a file or a decimal string
• initialize a few things
• loop over bits including mults, squarings, additions etc. including (special) mod reductions
• test a condition
• report result to screen and file

We have the source to LLR/PFGW/Prime95 but those are thousands of lines of code (and code for GUI). I envisage maybe 50 lines of simple code, which can be hacked.

As for Tony's x <- x^2-2 (LLT), I agree they are hardly faster than a fermat base 3 test

[danaj]

Originally Posted by R.D. Silverman

So why is it in a sub-forum for discussion of mathematics????

My two kopeks. There are a few different topics going on, and I'm not sure if you mean the first or second is inappropriate.

1) T.Rex's idea of a L-L type test. That's seemingly the point of the thread. I get different impressions from comments as to how useful this is vs. current PRP tests, which would seem to be something worth discussing.

2) the digression to gwnum programs. It came up because of the subject matter, and isn't directly math related.

batalov: thanks, though I was hoping for a simple gwnum program, not LLR.

[R.D. Silverman]

Originally Posted by danaj

My two kopeks. There are a few different topics going on, and I'm not sure if you mean the first or second is inappropriate.

1) T.Rex's idea of a L-L type test. That's seemingly the point of the thread. I get different impressions from comments as to how useful this is vs. current PRP tests, which would seem to be something worth discussing.

Worth discussing? Fine.

But the discussion contains no mathematics. I don't even see a discussion of a heuristic which suggests WHY
the test reveals PRPs. LL works for a reason. If T.Rex wants to suggest that the test is useful he needs to
provide at least some mathematics as to WHY numbers that pass it might be prime.

2) the digression to gwnum programs. It came up because of the subject matter, and isn't directly math related.

NONE of it contains mathematics.

[T.Rex]

Originally Posted by R.D. Silverman

Worth discussing? Fine.

But the discussion contains no mathematics.

NONE of it contains mathematics.

Yes. These threads contain NO mathematics. FOR NOW. It is now your duty to start finding ideas for proving these conjectures with Math tools, like I did for the Reix-Vrba algorithm (but found only the first part of the proof).

I put this in Math threads because it deals with possible primality-proof methods that need Math proof. Go and work !

If you had read in depth books about old math genius people, you should know that FIRST they did experimental computation by hand. Then, with facts, they started to prove what were conjectures at first.
They were genius people due to several qualities : be curious, experiment a lot with pen and paper, then search and find proofs.

In any case, this is fun !

[R.D. Silverman]

Originally Posted by T.Rex

Yes. These threads contain NO mathematics. FOR NOW. It is now your duty to start finding ideas

MY duty??? What the fuck have you been smoking??? You are the one presenting this as a valid PRP test.
It is YOUR responsibility to provide supporting mathematics.

I put this in Math threads because it deals with possible primality-proof methods that need Math proof. Go and work !

I have ZERO interest.

If you had read in depth books about old math genius people, you should know that FIRST they did experimental computation by hand. Then, with facts, they started to prove what were conjectures at first.
They were genius people due to several qualities : be curious, experiment a lot with pen and paper, then search and find proofs.

In any case, this is fun !

Hey moron!


I don't NEED to read books about them. In many cases I am on a first name basis with them.
I have collaborated with them.

You say "experiment a lot.... then find proofs". But one needs a least some supporting heuristical
arguments that suggest looking for a proof would have some chance of succeeding. The people of whom
you speak don't just pull a test from their ass. They have some reason for believing it might be correct.

All this thread has produced is mindless numerology. It contains no mathematical arguments at all.

I would like to see an explanation of why a number passing your test(s) has a reason that we should
expect it to be prime. You are one making the proposal(s). It is YOUR job to present supporting arguments.
[and saying that it works for a small set of numbers you tried is not a supporting argument]

Do you even know what group you might be working in, or its order as a function of the number being
tested? (Hint: I do)

[T.Rex]

Dear Silverman
You are still the same ! It's nice to see that some things are stable in this so moving world.
And you still don't read your comments twice in order to see when you are wrong. By providing these algorithms, I've provided heuristical arguments proving that there is something interesting behind that people should study and find a math theory for explaining why it works: properties of a DiGraph under x^2-2 modulo N. Remember that my algorithm Reix-Vrba for Wagstaff numbers has been used for finding the biggest known PRPs : (2^13372531+1)/3 and (2^13347311+1)/3 . See: http://www.primenumbers.net/prptop/prptop.php
Anyway, I've already produced Math papers about proof of LLT for Mersenne and Fermat numbers. I also worked on building a proof for the conjecture for LLT for Wagstaff numbers, with some gentle help from Hugh C. Williams. And I'm not a professional in Math, as you seems to be.
Read Edouard Lucas books and papers, read Hugh C. Williams book about Lucas' work, read Ribenboim, read all the books and papers about this subject, read my papers, and then go back with a proof, so that you can prove you can do something useful rather than always saying that other people are nuts.
Have a good day.

[Batalov]

Originally Posted by T.Rex

Remember that my algorithm Reix-Vrba for Wagstaff numbers has been used for finding the biggest known PRPs : (2^13372531+1)/3 and (2^13347311+1)/3 . See: http://www.primenumbers.net/prptop/prptop.php

Are you sure it was not a simple ABC ($a*$b^$c$d)/$e test in llr?

[paulunderwood]

Originally Posted by Batalov

Are you sure it was not a simple ABC ($a*$b^$c$d)/$e test in llr?

DRUG (Diepeveen-Reix-Underwood-Gilchrist) used Reix-Vrba up to exponent 10M. Ryan Propper said that he used "PFGW -f" to find the top 2 PRPs.

[Batalov]

Same thing: P95, llr, pfgw all use the same library and the same FFT mod (2^n+1) with the gcd(res, (2^n+1)/3) in the last iteration only.
As for his use of -f the only thing one can say is