Alleged Humongous Prime Number Thread #117
 

I found a prime number with an exponent 10 digits long. I didn't find the exponent using Prime95, I simply attempted to confirm it wth Prime 95; apparently 10 digits is one too long because I am unable to test it. However, I am completely positive the equation represents a prime number of at least 100 million digits, but I do not know where to submit it. Where do I turn it in for testing and awarding?

I don't know that anyone would be willing to test it for you, because there's no particular reason to believe your claim. You haven't given any evidence, let alone a proof.

If you want people to donate their knowledge and CPU time, you'll probably have to be more convincing.

The reason that I'm not giving any evidence is because I don't want my prime number to be stolen. I'm fairly new to this particular program; I don't exactly know how to test/code my prime numbers. The reason I joined is BECAUSE I found this large, as well as many others. I also have several different theories; all I ask before I submit my results and evidence is a program that factors/calculates large prime numbers to download.

Does anyone know of any such program? If you could give me the location where I could download one, I'll submit my results shortly after I get my test results back; I feel that Prime95 is too complicated and I need a standard prime calculator program.

[quote=CR24;175427] Where do I turn it in for testing and awarding?[/quote]If you're referring to the EFF award, the one mentioned in the prime95 documentation, see [URL]http://www.eff.org/awards/coop[/URL] for more information. Be sure to read the official rules at [URL]http://w2.eff.org/awards/coop-prime-rules.php[/URL]

Especially note rule 4F:
[quote]Your claim must include a citation and abstract of a published paper that announces the discovery and outlines the proof of primality. The cited paper must be published in a refereed academic journal with a peer review process that is approved by EFF.

We strongly recommend that you submit your paper to an appropriate refereed academic journal of one of the following societies:
[LIST][*] [URL="http://www.ams.org/"]American Mathematical Society[/URL][*] [URL="http://www.austms.org.au/"]Australian Mathematical Society[/URL][*] [URL="http://camel.math.ca/"]Canadian Mathematical Society[/URL][*] [URL="http://www.lms.ac.uk/"]London Mathematical Society[/URL][*] [URL="http://www.maa.org/"]Mathematical Association of America[/URL][/LIST] Note that not all publications of the above societies are appropriate refereed academic journals. Questions about the appropriateness of a journal should be directed to the EFF computation award question address (see rule #9 below).

[B]IMPORTANT: The EFF will reject any claim that fails to provide a citation and abstract of a published paper that announces the discovery and outlines the proof of primality.[/B]
[/quote]That means that you will have to publish your result in a paper in a refereed academic journal with a peer review process that is approved by EFF.

If you don't know what that means, you need to start learning what's involved. You won't get any money until after you've had your paper published; in fact, you can't even submit a claim to EFF for the award until after you've had your paper published.

Also, read the other rules carefully to see what sorts of information you'll need to document in order to qualify.

[quote]I found a prime number with an exponent 10 digits long.[/quote]So, the exponent is between 1 billion and 10 billion, right?

Is the prime number a Mersenne prime, or some other type?

If it's a Mersenne prime, of the form 2[sup]e[/sup]-1, where [I]e[/I] is the exponent, then that means it's between 2[sup]1,000,000,000[/sup]-1 and 2[sup]10,000,000,000[/sup]-1.

If it's some other type of prime, then what is its form (i.e., how is the exponent used in forming the number)?

Answering these questions in this forum won't endanger your claim [B]if[/B] you've documented all the information specified in the official EFF rules.

[QUOTE=CR24;175433]The reason that I'm not giving any evidence is because I don't want my prime number to be stolen. I'm fairly new to this particular program; I don't exactly know how to test/code my prime numbers. The reason I joined is BECAUSE I found this large, as well as many others. I also have several different theories; all I ask before I submit my results and evidence is a program that factors/calculates large prime numbers to download.[/QUOTE]

To understand my skepticism, you'd have to know that I've seen hundreds of claims (not an exaggeration!) like yours, none of which panned out. If yours does it will be the first such claim I've ever seen hold.

Also, for some reason, many/most of these baseless claims (not just about primes now) were from people with concerns about their work "being stolen". I'm not sure where that idea comes from -- mathematicians are more than happy to give credit where due.

[QUOTE=CR24;175433]Does anyone know of any such program? If you could give me the location where I could download one, I'll submit my results shortly after I get my test results back; I feel that Prime95 is too complicated and I need a standard prime calculator program.[/QUOTE]

You said that your number has "an exponent 10 digits long". I take that to mean your number is between one billion and ten billion bits long. With Prime95*, that would take roughly 5 to 100 years to check on current commodity hardware. With glucas* or mlucas* it would take 10 to 200 years. With a general program like Primo*, the universe would grow cold and dark long before it would finish.

* Suitable modified to work with numbers this large. Currently I know of no program that handles numbers this big.

I really don't think you need to worry about it being stolen. If you post it here, it will be recorded that you, CR24, (might want to provide your real name as well when/if you post it).
Anyway...
Is the number a Mersenne number? (2^p-1, p is a prime) I assume so since you want to use Prime95 to test it. Anything too large for Prime95 to test will take an [i]extremely[/i] long time (read: 'I hope you've got until-the-end-of-the-universe' long) to test in anything else. Have you tried checking for small factors? ECM? P-1? Anything?
You can use trial factoring, ECM, and P-1 with GMP-ECM. You can find compiled links for GPM-ECM and several other factoring programs for various OSs/CPUs at [url]http://gilchrist.ca/jeff/factoring/[/url]
If there's anything that will give you a probable prime (PRP) or prime determination on a number that big, (there probably is) it would take roughly an eternity.

[quote=CR24;175433]The reason that I'm not giving any evidence is because I don't want my prime number to be stolen.[/quote]That's a reasonable concern. So, follow the EFF rules about documentation. It's important to document the time/date you first proved the number is prime, the exact method you used to prove that the number is prime, and how long it took to do the proof.

Telling us the general mathematical type of the prime number, or the method you used to prove that the number is prime, won't give anyone enough information to steal yours.

[quote]I'm fairly new to this particular program; I don't exactly know how to test/code my prime numbers.[/quote]If you don't know how to test your prime numbers, then how do you know they're prime?

[quote]The reason I joined is BECAUSE I found this large, as well as many others. I also have several different theories; all I ask before I submit my results and evidence is a program that factors/calculates large prime numbers to download.[/quote]If you don't already have any program that can prove a particular number is a prime number, then how do you know your number is prime?

[quote]Does anyone know of any such program?[/quote]There are several, but each one works on only numbers of certain types (prime95 works on only Mersenne numbers, not other types). If you can't reveal what type (general mathematical form) your number is, you can't expect us to recommend which program you could use.

If you don't know how to describe what mathematical type your number is, you almost certainly are misunderstanding a lot of stuff and don't really have a multimillion-digit prime number.

[quote]If you could give me the location where I could download one, I'll submit my results shortly after I get my test results back; I feel that Prime95 is too complicated and I need a standard prime calculator program.[/quote]The other programs are no simpler than prime95; in fact, many are more complicated.

[QUOTE=Mini-Geek;175439]You can use trial factoring, ECM, and P-1 with GMP-ECM. You can find compiled links for GPM-ECM and several other factoring programs for various OSs/CPUs at [url]http://gilchrist.ca/jeff/factoring/[/url][/QUOTE]You can use Factor5 to Trial Factor the number upto a reasonable bit depth, too.

There are people on this board that will not "steal" your prime and can be trusted with the exponent. George would not 'steal' it.

BTW, if you know your exponent, you can calculate exactly how many digits long the number is. And one could figure out about how long it would take Prime95 to check the number.

If you really want to test a number this large, you're probably going to have to hire someone with access to a fast machine. Either publish it to stake your claim to the number, or else have a lawyer draft an appropriate confidentiality agreement.

[QUOTE=cheesehead;175440]Telling us the ... method you used to prove that the number is prime, won't give anyone enough information to steal yours.[/QUOTE]

It might - if the method was quick enough that using it would quickly turn up the prime.

Not that I believe his claim for a second...

Out of curiosity, how long would it take to run an ECM curve on a number that size? Say, B1 = 50,000.