Testing an expression for primality

[1260]

Can anyone recommend a software (windows-based) for testing the primality of a given mathematical expression? Most that I know of are for specific types of primes. (e.g. fermat, mersenne).

-- Ray

[ewmayer]

A google search for "general purpose primality proving software" turns up the following page:

http://directory.google.com/Top/Science/Math/Number_Theory/Prime_Numbers/Primality_Tests/Primality_Proving/Software/

which has links to all the relevant such programs.

[rogue]

Try WinPFGW (there is also a linux version available). It is based upon George's FFT code used in the GIMPS project. It can do both PRP and primality testing.

Although the project is open source, nobody has been able to write a version of PFGW that can run on other non-x86 CUPs.

[1260]

Thanks.

[pakaran]

WinPFGW is somewhat limited in proving primality of numbers which don't have special forms... for that you might want to try one of the other linked programs.

[1260]

Yes, I'm now using WinPFGW, and it has the option to evaluate an expression for primality, aside from those of special forms. It's not that limited after all.[/i]

[stathmk]

I have a question about which software is the most appropriate or fastest for proving. I thought that this thread is the most appropriate. But this thread may be forgotten or outdated after 12 years?

Go to http://primes.utm.edu/primes/search.php . Where it says digits, put in 411101 for the minimum and 411101 for the maximum. Click on “Search database for matches.” The result shown would be somebody’s discovery of 1874512^65536+1. I spent months sieving in NewPGen for k*1874512^65536+1 where k is a number between 2 and 400,000,001. It’s now sieved past 140.7 trillion. My understanding or misunderstanding was that Generalized Fermats must be easier to discover if there are more primes of this type than any others in Chris Caldwell’s Top 5000 database. I also wanted to see if I could discover an arithmetic progression this way. I’m running Windows Vista and since July 7, I’m only in line 89 in OpenPFGW. Is OpenPFGW, Prime95, LLR, or something else the fastest prover for NewPGen results for Windows Vista for Chris Caldwell’s Top 5000 list? That is what I please would like to know.

EDIT: There’s another reason why I sieved above 400,000 digits and chose something based off of 1874512^65536+1. I wanted to find a prime with more than “401k” (401*1024 or 410,624) digits.

[R.D. Silverman]

Originally Posted by stathmk

My understanding or misunderstanding was that Generalized Fermats must be easier to discover if there are more primes of this type than any others in Chris Caldwell’s Top 5000 database.

Huh? What is this? Start with the following:

You say Generalized Fermat's must be easier to discover". Easier than WHAT?

You also say "if there are more primes of this type than any other... in the datbase". Why don't you just count them?
Then you will know rather than asking "if". There are either more primes of this type of there aren't. There is no "if"

Finally one must ask why having more primes of a given type in a given database means that they must be easier to find. How does one reach this conclusion? It could also mean "the tools people have are amenable to primes of this type but not other types".

In CS, "easier" means "has lower time complexity". Is this what you mean?

I also wanted to see if I could discover an arithmetic progression this way.

Discovering an AP is trivial. What do you really mean here?

Your terminology is not well defined.

[stathmk]

Originally Posted by R.D. Silverman

Huh? What is this? Start with the following:

You say Generalized Fermat's must be easier to discover". Easier than WHAT?

You also say "if there are more primes of this type than any other... in the datbase". Why don't you just count them?
Then you will know rather than asking "if". There are either more primes of this type of there aren't. There is no "if"

Finally one must ask why having more primes of a given type in a given database means that they must be easier to find. How does one reach this conclusion? It could also mean "the tools people have are amenable to primes of this type but not other types".

In CS, "easier" means "has lower time complexity". Is this what you mean?



Discovering an AP is trivial. What do you really mean here?

Your terminology is not well defined.

As of today, if I go to http://primes.utm.edu/primes/search.php and type in Generalized Fermat, then it returns 4439 results. If I do the same thing and just type in Fermat, then it returns 4519 results. I meant that there are more primes discovered of this type than any other on Chris Caldwell’s List.

I meant that they would take less time to discover. If you want to call it lower time complexity, then fine.

I know discovering an arithmetic progression is trivial or superfluous. If I discover one then it’s a happy accident. Somebody discovered that 1874512^65536+1 is prime, so if I discover that k*1874512^65536+1 is prime then I’ll see if there’s a progression. I doubt if this progression will be discovered, but I’m searching for this as an afterthought.

This seems to be the first time we’ve heard of each other and I had forgotten to mention something. Go to http://www.primenumbers.net/prptop/prptop.php , scroll down, where it says find by discoverer, select Matt Stath, and I have found 49 probable primes in the past. The top 2 that I discovered with over 40,000 digits were with NewPGen and OpenPFGW. After being on Henri & Renaud Lifchitz’ List, I’m trying to be on Chris Caldwell’s List.

My question is still about whether OpenPFGW, Prime95, LLR, or something else would be the fastest prover. However, Jean Penne’s LLR has discovered 4,854 primes at http://primes.utm.edu/bios/top20.php...&by=PrimesRank . I’m going to test for a least a day to find out if LLR or Prime95 are faster than OpenPFGW. If anybody else is reading this and cares to respond about a program that is faster, then please do.

EDIT: I had forgotten to mention that according to http://primes.utm.edu/top20/page.php?id=14 , I'm aiming too high with too many digits for an arithmetic progression.

[paulunderwood]

Originally Posted by stathmk

My question is still about whether OpenPFGW, Prime95, LLR, or something else would be the fastest prover. However, Jean Penne’s LLR has discovered 4,854 primes at http://primes.utm.edu/bios/top20.php...&by=PrimesRank . I’m going to test for a least a day to find out if LLR or Prime95 are faster than OpenPFGW. If anybody else is reading this and cares to respond about a program that is faster, then please do.

They all use the latest Woltman library -- so using any should be fine. What you should investigate are the sieves used

[rogue]

Originally Posted by stathmk

I have a question about which software is the most appropriate or fastest for proving. I thought that this thread is the most appropriate. But this thread may be forgotten or outdated after 12 years?

Go to http://primes.utm.edu/primes/search.php . Where it says digits, put in 411101 for the minimum and 411101 for the maximum. Click on “Search database for matches.” The result shown would be somebody’s discovery of 1874512^65536+1. I spent months sieving in NewPGen for k*1874512^65536+1 where k is a number between 2 and 400,000,001. It’s now sieved past 140.7 trillion. My understanding or misunderstanding was that Generalized Fermats must be easier to discover if there are more primes of this type than any others in Chris Caldwell’s Top 5000 database. I also wanted to see if I could discover an arithmetic progression this way. I’m running Windows Vista and since July 7, I’m only in line 89 in OpenPFGW. Is OpenPFGW, Prime95, LLR, or something else the fastest prover for NewPGen results for Windows Vista for Chris Caldwell’s Top 5000 list? That is what I please would like to know.

EDIT: There’s another reason why I sieved above 400,000 digits and chose something based off of 1874512^65536+1. I wanted to find a prime with more than “401k” (401*1024 or 410,624) digits.

What is your goal? It seems to me that you want to find a prime that will be on the Top 5000. You have a number of choices. If you don't want to get your hands too dirty, then participate in one of the projects that just require you to download a client and start it. If you want to do more of the work yourself, then it depends upon if you want to sieve. Some projects have pre-sieved ranges of numbers to test and others do not.

If you wan to get a number in the Top 5000 ASAP, then it will require a bit of luck as there are a number of factors including: how many people are searching (if a distributed project), how large a prime do you want to find, what sieving software is available, what PRPing software is available, can primality be proven, how much horsepower you can dedicate to the search, do you have a GPU. I'm certain there are many other factors that I haven't even listed.