Hi, how can I test my probable prime number?
 

Hi, how can I test my probable prime number?
Thanks..

GO FOR IT!
 

Run Prime95 on it. :smile:
Since you see a probability of its being prime, don't bother with Trial Factoring or P-1 Factoring. However, unless you are actually Curtis Cooper incognito, there is probable disappointment in your future. :davieddy:

[B][SIZE=3]Good Luck! [/SIZE][/B]:rolleyes:

how big? test it for what?

We'll need more information to help you and tell you if it's even feasible (with hardware available today). How large is it? What form is it? (e.g. 2^p-1, n!-1, 2^n+b, etc.; you don't have to tell us the exact number if you don't want to, but at least give us an idea of the scale of the number(s) involved) (some numbers with special forms have fast tests, like the LL for Mersenne numbers, while others require a more difficult algorithm, ECPP, that can be run on a number of general form) If the factorization of N-1 or N+1 (where your number is N) is known, you can run a fast test.

Possibilities include Prime95, PFGW, and Primo (ECPP).

(I'm assuming you're saying that you have a number that has already passed a PRP, probable prime, test, and you want to know how to prove it prime)

though nothing else was revealed:

[url]http://mersenneforum.org/showpost.php?p=372937&postcount=4[/url]

[QUOTE=science_man_88;372967]though nothing else was revealed:

[URL]http://mersenneforum.org/showpost.php?p=372937&postcount=4[/URL][/QUOTE]

bad link

What is the point of asking a question here, if you are going to ignore all the follow-up posts?

[QUOTE=BudgieJane;373254]What is the point of asking a question here, if you are going to ignore all the follow-up posts?[/QUOTE]

A bot posting?

[QUOTE=BudgieJane;373254]What is the point of asking a question here, if you are going to ignore all the follow-up posts?[/QUOTE]How do you know the OP ignored the replies? Perhaps the OP read them/is reading them now and is taking notice, or waiting for what he/she considers a sensible response?

[QUOTE=retina;373258]How do you know the OP ignored the replies? Perhaps the OP read them/is reading them now and is taking notice, or waiting for what he/she considers a sensible response?[/QUOTE]

Or he/she did not understand what he/she was asking and does not
understand the replies.

[QUOTE=R.D. Silverman;373269]Or he/she did not understand what he/she was asking and does not
understand the replies.[/QUOTE]Yes, perhaps. Often people post to several boards at the same time. They get belittled on one board, ignored on a second board, and nanny coddled on a third. It doesn't take a genius to guess which board they direct their attention to.

[QUOTE=retina;373271]Yes, perhaps. Often people post to several boards at the same time. They get belittled on one board, ignored on a second board, and nanny coddled on a third. It doesn't take a genius to guess which board they direct their attention to.[/QUOTE]

Yep.

But I saw none of that here. The OP received honest, reasonable replies.

I did try this program. Got the basic idea then the computer died. Good stress test. Lol.

OP said he had a specific number. Second person said put it in prime95. How do I put a specific number in? I'm looking at playing with 6^n +/- 1

Is there a way to put a certain number of that form or can I manipulate the programs search to leave the 2^n and just use 6^n

Thank you

Don't need to bother with 6^n-1, that is always divisible by 5. (why?)
:smile:

Don't need to bother with 6^n+1, either. It can only be prime when n=2^m (for bonus points, -- why?)

And even then, after the first three primes (7, 37 and 1297), probabilistically, -- never. See [URL="http://www.prothsearch.net/GFN06.html"]http://www.prothsearch.net/GFN06.html
[/URL]


P.S. [B]But[/B] you can search for factors of these. You will be in an awesome company, too! Look: H.Riesel, W.Keller, H.Dubner, and many other interesting people. One tool for that is [URL="http://www.mersenneforum.org/mmff-gfn/"]mmff-gfn[/URL] (on a GPU) and there are other programs.

And in general, unless I'm mistaken, prime95 is specifically designed, written, and highly optimised, for testing the primality of numbers of the form 2^n-1 and cannot be used for other numbers.

[QUOTE=Brian-E;384666]And in general, unless I'm mistaken, prime95 is specifically designed, written, and highly optimised, for testing the primality of numbers of the form 2^n-1 and cannot be used for other numbers.[/QUOTE]

Correct, as far as [B]primality[/B] tests go. But it can do a PRP-test on a much larger set of numbers, (k*b^n+/-c)/f

[QUOTE=axn;384669]Correct, as far as [B]primality[/B] tests go. But it can do a PRP-test on a much larger set of numbers, (k*b^n+/-c)/f[/QUOTE]
Ah, thanks. I never even knew about PRP testing with Prime95. I do now.:smile:

[QUOTE=Batalov;384658]Don't need to bother with 6^n+1, either. It can only be prime when n=2^m (for bonus points, -- why?)

And even then, after the first three primes (7, 37 and 1297), probabilistically, -- never. See [URL="http://www.prothsearch.net/GFN06.html"]http://www.prothsearch.net/GFN06.html
[/URL]


P.S. [B]But[/B] you can search for factors of these. You will be in an awesome company, too! Look: H.Riesel, W.Keller, H.Dubner, and many other interesting people. One tool for that is [URL="http://www.mersenneforum.org/mmff-gfn/"]mmff-gfn[/URL] (on a GPU) and there are other programs.[/QUOTE]


Thank you. I'll look that up.
I know 6^n-1 is always a product of 5 but wanted to play with numbers like
6^n - 6^n-1 - 6^n-2..... -6^0
I've got a working sieve for elimination of all composite numbers and wanted to run tests against it.

[QUOTE=jonno;384721]Thank you. I'll look that up.
I know 6^n-1 is always a product of 5 but wanted to play with numbers like
6^n - 6^n-1 - 6^n-2..... -6^0
I've got a working sieve for elimination of all composite numbers and wanted to run tests against it.[/QUOTE]
When you are using forms like these, all you will get will be probable primes.
You don't need to reinvent the wheel for a sieve for this form either, because it is easily simplified:
6^n - 6^n-1 - 6^n-2..... -6^0 = 6^n - (6^n-1)/5 = (4*6^n+1)/5
for which srsieve package will be vastly faster than any sieve you can write.
You need to sieve with "-pmin 7" (and then remove n=1(mod 5) because these are divisible by 5^k with k>1; except the only prime divisible by 5 at n=1, which is 5); and additionally remove all n=0 (mod 4) because of the Aurifeuillian factorization:
(4*6^4m+1)/5 = (2 * 6^2m + 2*6^m + 1)/5 * (2 * 6^2m - 2 * 6^m + 1).

And then you will find some PRPs with pfgw. Here is how they will start:
[CODE](4*6^1+1)/5 is prime
(4*6^2+1)/5 is prime
(4*6^3+1)/5 is prime
(4*6^5+1)/5 is prime
Switching to Exponentiating using GMP
(4*6^15+1)/5 is 3-PRP! (0.0000s+0.0001s)
(4*6^25+1)/5 is 3-PRP! (0.0000s+0.0014s)
(4*6^29+1)/5 is 3-PRP! (0.0000s+0.0011s)
(4*6^73+1)/5 is 3-PRP! (0.0000s+0.0000s)
(4*6^90+1)/5 is 3-PRP! (0.0000s+0.0000s)
(4*6^139+1)/5 is 3-PRP! (0.0001s+0.0000s)
(4*6^194+1)/5 is 3-PRP! (0.0001s+0.0000s)
Switching to Exponentiating using Woltman FFT's
(4*6^242+1)/5 is 3-PRP! (0.0016s+0.0000s)
(4*6^939+1)/5 is 3-PRP! (0.0161s+0.0000s)
(4*6^3518+1)/5 is 3-PRP! (0.2101s+0.0000s)
(4*6^3963+1)/5 is 3-PRP! (0.2434s+0.0001s)
(4*6^4694+1)/5 is 3-PRP! (0.3930s+0.0000s)
(4*6^5570+1)/5 is 3-PRP! (0.5256s+0.0001s)
(4*6^5615+1)/5 is 3-PRP! (0.5309s+0.0000s)
(4*6^6702+1)/5 is 3-PRP! (0.8243s+0.0000s)
(4*6^13962+1)/5 is 3-PRP! (3.8427s+0.0001s)
(4*6^14269+1)/5 is 3-PRP! (3.9239s+0.0001s)
(4*6^16339+1)/5 is 3-PRP! (4.6013s+0.0001s)
(4*6^16882+1)/5 is 3-PRP! (5.0966s+0.0001s)
...[/CODE]
Nice series, pretty dense (at least at its start).

All of these you can prove with Primo, but the larger ones will become unfeasible to prove, so the best place they will go to will be the PRP Top. The new PRP Top cutoff to enter is 20,000 decimal digits, so you'd need n>25702...
[CODE](4*6^22582+1)/5 is 3-PRP! (7.0355s+0.0001s)
(4*6^31415+1)/5 is 3-PRP! (13.1867s+0.0002s)
(4*6^105554+1)/5 is 3-PRP! (183.1141s+0.0005s) (82137 digits)
(4*6^120749+1)/5 is 3-PRP! (218.7588s+0.0006s) (93961 digits)
...
[/CODE]

These are "near-repunits 444...445 in base 6". I've created an OEIS sequence [URL="http://oeis.org/A248613"]A248613[/URL] for it. Feel free to find additional terms.

[QUOTE=retina;373271]Yes, perhaps. Often people post to several boards at the same time. They get belittled on one board, ignored on a second board, and nanny coddled on a third. It doesn't take a genius to guess which board they direct their attention to.[/QUOTE]
Where are these nanny-coddling boards? I've never encountered one.

It's the internet, the masks come off, and people, including myself, are revealed as their true selves.

[QUOTE=jasong;384806]Where are these nanny-coddling boards? I've never encountered one.[/QUOTE]Maybe some people act in such a way that they never get nanny coddled?[QUOTE=jasong;384806]It's the internet, the masks come off, and people, including myself, are revealed as their true selves.[/QUOTE]So the protection of anonymity is at work? Except of course people are not really anonymous. With all the analysis and tracking going on it is almost impossible to remain anonymous without some very disciplined and restrictive behaviours.

[QUOTE]It's the internet, the masks come off, and people, including myself, are revealed as their true selves. [/QUOTE]

Au contraire. On the net, one can build all sorts of personae. While it may be different than in-person interaction, I doubt that one or the other is more true. As Mr Colbert would say, both are exercises in "truthiness". :wink: