Thread for posting tiny primes - Page 22

3.14159 · 2010-08-09, 16:18

Submissions:
New personal record: 22147 * 2²⁵⁶⁷²⁰ + 1 (77285 digits)
4785 * 2¹⁷⁵⁰⁰ + 1 (5272 digits)
54345 * 2³⁹⁸⁶⁰ + 1 (12004 digits)

3.14159 · 2010-08-09, 17:45

Submissions:
21158 * 144²⁸⁶⁰ + 1 (6178 digits)

Searching for k * 99792⁷⁵⁶⁰ + 1

Merfighters · 2010-08-28, 08:12

You know what?
The primes we called 'binary primes' already has a (bit complicated) name!

Just found this at the internet:
http://primes.utm.edu/lists/top_ten/topten.pdf - See page 6

Quote:

An anti-Yarborough prime can have any number of 1's and 0's only.

It saids that the largest known such prime (when that list was made) is: 10^30802+1110111*10^15398+1.

And I found this at Top5000: 10^78942+10111100100111101*10^39463+1

Here is all of them, less than 11 digits:

Code:

kar_bon · 2010-08-28, 08:50

Quote:

Originally Posted by Merfighters

Just found this at the internet:
http://primes.utm.edu/lists/top_ten/topten.pdf - See page 6

It's totally outdated!

Better use this link of the currently Top 20.

3.14159 · 2010-08-28, 12:19

Karsten, I must thank you for reviving the dead threads.

Submissions: (Marked in respective categories they are in.)
#2. 468550 * 1999⁵³⁴⁶ + 1 (17652 digits)
#2. 515361 * 1296⁵⁶⁸⁰ + 1 (17686 digits)
#2. 63483 * 10⁸⁴⁹⁰ + 1 (8495 digits)
#2. 570331 * 2⁹³⁵⁶⁰ + 1 (28170 digits)
#2. 7428 * 10¹³⁴⁵⁰ + 1 (13455 digits)
#2 + #8. 4034 * 1500⁴⁰³⁴ + 1 (12816 digits)
#1. 601969 * 2⁷⁸²⁹⁰ + 1 (23568 digits)
#3. 634 * 2480!² + 1 (14690 digits)
#2. 83529 * 48⁷⁸⁹⁰ + 1 (13270 digits)
#2. 159738 * 756⁹⁵⁷⁰ + 1 (27553 digits)
#7. 1364 * 4200! + 1 (13399 digits)
#3. 29220 * 6¹²⁸⁶⁰ + 1 (10012 digits)
#3. 2898 * 1201!⁴ + 1 (12720 digits)
#4. 703 * p(125)⁶⁶ + 1 (19104 digits)
#3. 12721 * 9!²⁵⁶⁰ + 1 (14238 digits)
#1. 3495 * 2²⁹⁶⁸⁰ + 1 (8939 digits)

3.14159 · 2010-09-02, 03:57

More submissions:

#2. 912646 * 798336²⁰¹⁶⁰ + 1 (118995 digits) + Largest PRP found by me.

Proving it is a whole different matter. No simple methods here. (Proth's only applies to base 2, if I remember correctly.)

3.14159 · 2010-09-02, 04:08

This thread will only buzz with some activity if I keep posting meager-sized primes.

Also: The PRP above is off of ECPP's range by a factor of 5 to 11.

3.14159 · 2010-09-02, 04:37

This might be more viable: 13963 * 10⁸⁹⁰⁰ + 1

Code:

13963*10^8900 + 1 may be prime. (a = 2)
13963*10^8900 + 1 is prime! (a = 3) [8905 digits]

Code:

13963000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000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is prime.

13963 is also prime!

Find me a larger example!

Mathew · 2010-09-02, 05:21

Primality testing 912646*798336^20160+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 35.70%
912646*798336^20160+1 is prime! (3212.3874s+0.0450s)

3.14159 · 2010-09-02, 05:24

Quote:

Originally Posted by Mathew Steine

912646*798336^20160+1 is prime! (3212.3874s+0.0450s)

Confirmed prime!

Also: 50740 * 10¹⁹⁷⁸⁰ + 1 is a PRP.

And, what program did you use? LLR?

Oh. WinPFGW.

Checking for false primes.

mdettweiler · 2010-09-02, 05:53

Quote:

Originally Posted by 3.14159

Confirmed prime!

Also: 50740 * 10¹⁹⁷⁸⁰ + 1 is a PRP.

And, what program did you use? LLR?

That's PFGW with the -t switch, which does an N-1 primality proof. N-1 is a little slower than a standard PRP test, but can consistently give a full proof of the primality of any number N when N-1 is trivially factorizable (as, for instance, in the case of a k*b^n+1 number). PFGW's -tp switch does an N+1 test, which is the analogue covering k*b^n-1 numbers.

FYI, this is also what Proth.exe uses for primality proofs such as 13963*10^8900+1 that you proved in post #239. It's not quite as fast as PFGW, but works on the same basic idea.

FYI #2: LLR uses a different proof of the N-1/N+1 tests for all non-base-2 k*b^n+-1 numbers (for which the LLR and Proth tests are not applicable). Its method allows it to perform a standard Fermat PRP test (a la PFGW) and then, if it returns PRP, build on the result directly to produce a proof (as opposed to an entirely separate test like PFGW does). Depending on various properties of the exact number in question, it can sometimes finish the proof with comparatively trivial additional calculation on top of the initial PRP; even in the worst case scenario, though (where it effectively has to run an additional PRP in another base in order to make the proof line up), it generally takes no more time than PFGW's total PRP+proof time.

From what I've observed of Proth.exe I have to wonder if it's actually doing the same thing as LLR (that is, a PRP test which is extended to form an N-1/N+1 proof) instead of the separate PRP and proof stages as exemplified by PFGW.

Anyway, to summarize all the above gobbledygook: if you find a PRP of the form k*b^n+-1, the quickest way to prove it is with PFGW's -t (+1) or -tp (-1) switches. Proth.exe will take somewhat longer, though can still work if you're going for the "antique proof program" category.

And LLR can be at least as efficient as PFGW if you want to do the whole search directly with it and have primes tested+proved all in one step.

2010-08-09, 16:18	#232
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Submissions: New personal record: 22147 * 2²⁵⁶⁷²⁰ + 1 (77285 digits) 4785 * 2¹⁷⁵⁰⁰ + 1 (5272 digits) 54345 * 2³⁹⁸⁶⁰ + 1 (12004 digits) Last fiddled with by 3.14159 on 2010-08-09 at 16:26

2010-08-09, 17:45	#233
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Submissions: 21158 * 144²⁸⁶⁰ + 1 (6178 digits) Searching for k * 99792⁷⁵⁶⁰ + 1 Last fiddled with by 3.14159 on 2010-08-09 at 17:46

2010-08-28, 12:19	#236
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Karsten, I must thank you for reviving the dead threads. Submissions: (Marked in respective categories they are in.) #2. 468550 * 1999⁵³⁴⁶ + 1 (17652 digits) #2. 515361 * 1296⁵⁶⁸⁰ + 1 (17686 digits) #2. 63483 * 10⁸⁴⁹⁰ + 1 (8495 digits) #2. 570331 * 2⁹³⁵⁶⁰ + 1 (28170 digits) #2. 7428 * 10¹³⁴⁵⁰ + 1 (13455 digits) #2 + #8. 4034 * 1500⁴⁰³⁴ + 1 (12816 digits) #1. 601969 * 2⁷⁸²⁹⁰ + 1 (23568 digits) #3. 634 * 2480!² + 1 (14690 digits) #2. 83529 * 48⁷⁸⁹⁰ + 1 (13270 digits) #2. 159738 * 756⁹⁵⁷⁰ + 1 (27553 digits) #7. 1364 * 4200! + 1 (13399 digits) #3. 29220 * 6¹²⁸⁶⁰ + 1 (10012 digits) #3. 2898 * 1201!⁴ + 1 (12720 digits) #4. 703 * p(125)⁶⁶ + 1 (19104 digits) #3. 12721 * 9!²⁵⁶⁰ + 1 (14238 digits) #1. 3495 * 2²⁹⁶⁸⁰ + 1 (8939 digits) Last fiddled with by 3.14159 on 2010-08-28 at 12:41

2010-09-02, 03:57	#237
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	More submissions: #2. 912646 * 798336²⁰¹⁶⁰ + 1 (118995 digits) + Largest PRP found by me. Proving it is a whole different matter. No simple methods here. (Proth's only applies to base 2, if I remember correctly.) Last fiddled with by 3.14159 on 2010-09-02 at 04:04

2010-09-02, 04:08	#238
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	This thread will only buzz with some activity if I keep posting meager-sized primes. Also: The PRP above is off of ECPP's range by a factor of 5 to 11. Last fiddled with by 3.14159 on 2010-09-02 at 04:22

2010-09-02, 05:21	#240
Mathew Nov 2009 2·5²·7 Posts	Primality testing 912646798336^20160+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 35.70% 912646798336^20160+1 is prime! (3212.3874s+0.0450s)

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