Thread for posting tiny primes - Page 23

3.14159 · 2010-09-02, 06:03

Thank you for the informative summary. Ah, that's how they're proved..

And, going for #20, sometime soon.

mdettweiler · 2010-09-02, 06:38

Here's a submission for the #2 category, found in an effort to prove the base 75 generalized Sierpinski conjecture:

3782*75^41086+1 is prime!

Alas, it cannot count for #20 as it was proven by LLR before I even saw it. It was found via PRPnet, a client/server primality testing program that I use to distribute work across multiple computers; PRPnet proves PRPs on the client end before even sending them to the server, and in this case since it used LLR as the worker application, it was in fact proven before the client program heard about it. So the chance to make this count for #20 was doubly absent.

Speaking of #20, though: where would I find a copy of the original PrimeForm? I have Proth.exe, but I'm wondering if PrimeForm would be faster (as ironic as it is to strive for quickness in what is essentially a waste of computing power given the faster software available today) since I could make it skip straight to an N-1/N+1 test instead of going through a whole PRP test first.

3.14159 · 2010-09-02, 14:34

Quote:

Originally Posted by Max

Speaking of #20, though: where would I find a copy of the original PrimeForm? I have Proth.exe, but I'm wondering if PrimeForm would be faster (as ironic as it is to strive for quickness in what is essentially a waste of computing power given the faster software available today) since I could make it skip straight to an N-1/N+1 test instead of going through a whole PRP test first.

You can download the original Primeform here.

It is not if you are applying for category 20.

Also: I'm testing that number, to ensure that you aren't bullshitting.

Code:

Special modular reduction using zero-padded FFT length 32K on 3782*75^41086+1
3782*75^41086+1 is 3-PRP! (168.2731s+0.0062s)

Applying N-1 test to definitely prove/disprove primality..

Code:

Primality testing 3782*75^41086+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using zero-padded FFT length 32K on 3782*75^41086+1
Calling Brillhart-Lehmer-Selfridge with factored part 74.55%
3782*75^41086+1 is prime! (169.8984s+0.0066s)

Excellent, you weren't lying. You have gained a spot for category 2 (Generalized Proth.)

I have sieved to 5.50 trillion for k * 2³²⁸⁷⁵⁰ + 1, 1.01 trillion for k * 28657²⁸⁶⁵⁷ + 1 (127737 and 98970 digits, respectively.)

mdettweiler · 2010-09-02, 16:42

Quote:

Originally Posted by 3.14159

You can download the original Primeform here.

It is not if you are applying for category 20.

Thanks. But I'm not sure what you mean by the second sentence...do you mean that it isn't faster than Proth.exe? Or that it isn't eligible for category #20 (antique proof program)?

Quote:

Also: I'm testing that number, to ensure that you aren't bullshitting.

Code:

Special modular reduction using zero-padded FFT length 32K on 3782*75^41086+1
3782*75^41086+1 is 3-PRP! (168.2731s+0.0062s)

Applying N-1 test to definitely prove/disprove primality..

Code:

Primality testing 3782*75^41086+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using zero-padded FFT length 32K on 3782*75^41086+1
Calling Brillhart-Lehmer-Selfridge with factored part 74.55%
3782*75^41086+1 is prime! (169.8984s+0.0066s)

Excellent, you weren't lying. You have gained a spot for category 2 (Generalized Proth.)

Nah, I'd have no reason to lie. But a verification is good anyway--since this prime wasn't big enough to get into the top-5000 list, it didn't get the top-5000 site's external verification, so I was effectively taking the word of the computer that found it.

And, would you know, another #2 entry popped up a few hours later:

2336*75^43523+1 is prime!

This one was found on a different machine via the same PRPnet server. It was found and proven with PFGW (first a PRP test, then an N-1 test run automatically by the PRPnet client).

3.14159 · 2010-09-02, 18:38

Quote:

Originally Posted by Max

Thanks. But I'm not sure what you mean by the second sentence...do you mean that it isn't faster than Proth.exe? Or that it isn't eligible for category #20 (antique proof program)?

Sorry for the ambiguity. I meant, it is not a waste of computing power if you want to apply for item 20: Obsolete-tech proven primes.

Quote:

Originally Posted by Max

And, would you know, another #2 entry popped up a few hours later:

2336*75^43523+1 is prime!

Let us run under the assumption that you are lying.

Immediately running N-1 test...

We are sorry: It is composite. It has divisors 33324686916885236022783006469, 396728734395838423566897342338803, and 6842588252918096856185211780024433747.

Nah, just pulling your chain! (Though it is semi-obvious.)

It's a proven prime number.

Code:

Primality testing 2336*75^43523+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Special modular reduction using zero-padded FFT length 40K on 2336*75^43523+1
Calling Brillhart-Lehmer-Selfridge with factored part 74.55%
2336*75^43523+1 is prime! (235.7026s+0.0111s)

Gained another spot for category 2. (Generalized Proth)

3.14159 · 2010-09-02, 19:07

Also: What is the easiest script to write for PFGW?

Trial division to prove primality of tiny primes? (1-10 digits)

Dammit. I think I accidentally deleted that script tutorial..

3.14159 · 2010-09-03, 01:13

Current sieve progress: 9.09 trillion for k * 2³²⁸⁷⁵⁰ + 1; 1.67 trillion for k * 28657²⁸⁶⁵⁷ + 1

3.14159 · 2010-09-04, 17:03

Reporting in for #18, General Cofactor: (1763085111 * 6²⁸⁰⁰ + 1)/889453 (2183 digits)

Batalov · 2010-09-04, 21:01

4*17¹⁷⁸⁴³⁸+1, a small new Generalized Fermat prime.

mdettweiler · 2010-09-04, 21:10

Quote:

Originally Posted by Batalov

4*17¹⁷⁸⁴³⁸+1, a small new Generalized Fermat prime.

I wouldn't exactly call it small...it's 219561 digits, more than enough to get into the top-5000 (at a rank of <1500th place) even without being a GFN!

Congratulations!

(Ironically enough, in this thread it only gets a #2 award, i.e. Generalized Proth, since there isn't a category for Generalized Fermat.)

BTW, was this found as an "extra bonus" from a CRUS search, or did you search specifically for a GFN?

Batalov · 2010-09-04, 21:39

Well, just a side trip, yeah. Just for fun^TM.

There was an interesting tiny missed 4*10^n+1 prime reported just last week, so I re-checked 4*10^n+1 to 200K and decided to poke at other bases. Sieving left this base (17) very well battered, so I though, why not... and pfgw'd the series. I am checking b=23 as well for the same form to 200K.

2010-09-02, 19:07	#248
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Also: What is the easiest script to write for PFGW? Trial division to prove primality of tiny primes? (1-10 digits) Dammit. I think I accidentally deleted that script tutorial.. Last fiddled with by 3.14159 on 2010-09-02 at 19:35

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2010-09-02, 06:03	#243
3.14159 May 2010 Prime hunting commission. 3220₈ Posts	Thank you for the informative summary. Ah, that's how they're proved.. And, going for #20, sometime soon.

2010-09-02, 06:38	#244
mdettweiler A Sunny Moo Aug 2007 USA (GMT-5) 3×2,083 Posts	Here's a submission for the #2 category, found in an effort to prove the base 75 generalized Sierpinski conjecture: 3782*75^41086+1 is prime! Alas, it cannot count for #20 as it was proven by LLR before I even saw it. It was found via PRPnet, a client/server primality testing program that I use to distribute work across multiple computers; PRPnet proves PRPs on the client end before even sending them to the server, and in this case since it used LLR as the worker application, it was in fact proven before the client program heard about it. So the chance to make this count for #20 was doubly absent. Speaking of #20, though: where would I find a copy of the original PrimeForm? I have Proth.exe, but I'm wondering if PrimeForm would be faster (as ironic as it is to strive for quickness in what is essentially a waste of computing power given the faster software available today) since I could make it skip straight to an N-1/N+1 test instead of going through a whole PRP test first.

2010-09-03, 01:13	#249
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Current sieve progress: 9.09 trillion for k * 2³²⁸⁷⁵⁰ + 1; 1.67 trillion for k * 28657²⁸⁶⁵⁷ + 1

2010-09-04, 17:03	#250
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Reporting in for #18, General Cofactor: (1763085111 * 6²⁸⁰⁰ + 1)/889453 (2183 digits)

2010-09-04, 21:01	#251
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	4*17¹⁷⁸⁴³⁸+1, a small new Generalized Fermat prime.

2010-09-04, 21:39	#253
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Well, just a side trip, yeah. Just for fun^TM. There was an interesting tiny missed 410^n+1 prime reported just last week, so I re-checked 410^n+1 to 200K and decided to poke at other bases. Sieving left this base (17) very well battered, so I though, why not... and pfgw'd the series. I am checking b=23 as well for the same form to 200K.