Thread for posting tiny primes - Page 84

wblipp · 2010-12-28, 14:08

Quote:

Originally Posted by lorgix

Is anyone factoring 17^n+1?

Richard Brent has tables of factors of a^n +/- 1 for a and n < 10000. The largest exponent with a published factor of this form is for 17^210+1. So either there is no systematic search or the factors are not being reported to him. OddPerfect's factoring of Vanishing Fermat Quotients has a factor for 17^47822552335+1.

William

lorgix · 2010-12-28, 14:49

Thanks.

The following two are extremely likely to be two-way splits.
17^213+1= ... P74.C129
17^228+1= ... P52.C118

The following two composites have no factors of 30digits or less.
17^222+1= ... P29.C174
17^243+1= ... P34.C133

lorgix · 2011-01-12, 16:50

I could have sworn I saw this proof this one time... Something about there being an infinite number of primes.

Yet this thread is slowing to a stop.

Also, in the interest of fairness; we should have a Composite posting thread.

3.14159 · 2011-01-25, 20:24

Okay.. I haven't submitted anything in a long time..

Here's another prime for you all..

31240951024194*128^3789+1 (7998 digits)

Primality testing 31240951024194*128^3789+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using generic reduction FFT length 2560 on 31240951024194*128^3789+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.84%
31240951024194*128^3789+1 is prime! (3.1410s+0.0009s)

≈pi seconds! That's nice. Luckily I have all my prime-searching stuff to continue onwards with.

3.14159 · 2011-01-25, 21:16

Another prime for you all;

756223*66^4600+1 (8376 digits);

Primality testing 756223*66^4600+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Special modular reduction using zero-padded FFT length 3584 on 756223*66^4600+1
Calling Brillhart-Lehmer-Selfridge with factored part 57.19%
756223*66^4600+1 is prime! (1.8654s+0.0274s)

3.14159 · 2011-01-31, 17:34

A prime composed of primes 401 and 409;

401409401409401401409409409409401409401409409401409401409409409401409409409401409409409401401.

A larger prime composed of primes 5087,3779,3691,3061,4933,1451,5849,4289,4547,9907,2579,1459, and 4159;

Code:

45474289145114514547493337791459377942894547508730611451584914591451584941593779584937795849306142894933990730615849454730613061377914515087454742895087584936913061493349334289306130614933990737795087257941593691428945479907584950871451145949333779493341594933508758495087508737791451306114593061145941593061415914591451415942894933508741594159428930614159377914591451415925794547508725794933306125791459493342893691454736914547493330613691990725793691508758493061454745474933428914514289584945474289428925793061145930613691508749331451145949334159454741591459257950879907257914594547369149334289145150873779584942894289257937792579428958495849306114514159454742894159145914592579369150872579990730613691454750874933508736912579415936913061306114514547377958492579990725794289493349334933377945473061369137791451454736913691377958492579428937799907257949335849493358499907584949335087145114514289257937791459428950873779369149331451990725794159428958494159454749333779508745473691145199075087508741594933428945472579145137799907145941599907145925791459145130613061990725795849145941593779306136915849306142891459493330619907454799073691257942892579493349334159145950873061257941595849257914593779415949334547145136914159584945474159257941599907415914591451493350875087584958495087145936911459428999079907257914591451990737793691454741594933454799073691306125791451145149334159145145474159454745471451454714514159306125794933415914595087145130611451257941593061

Batalov · 2011-02-02, 04:41

4*107^32586+1 is a prime and a Generalized Fermat, too

3.14159 · 2013-09-20, 04:24

Since the last thread died a slow and terrible death/bumping dead threads = bad forum etiquette..

Prime posting time to lighten the mood/bring some activity to a semi-dead board/my "home board"?

"rules"
1. Anything ≥ 5000 digits is good.

In any event, bumping with some kbbs:

57787*5256⁵²⁵⁶+1 (19561 digits)
Running N-1 test using base 5
Special modular reduction using zero-padded AMD K10 type-0 FFT length 12K, Pass1=48, Pass2=256 on 57787*5256^5256+1
Calling Brillhart-Lehmer-Selfridge with factored part 50.07%
57787*5256^5256+1 is prime! (33.2498s+0.0184s)

67000*5256⁵²⁵⁶+1 (19561 digits)
Running N-1 test using base 23
Special modular reduction using zero-padded AMD K10 type-0 FFT length 12K, Pass1=48, Pass2=256 on 67000*5256^5256+1
Calling Brillhart-Lehmer-Selfridge with factored part 50.07%
67000*5256^5256+1 is prime! (32.7381s+0.0103s)

More bumping:
38247*2³⁵⁵⁰⁰+1 (10692 digits)
Primality testing 38247*2^35500+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using all-complex FFT length 3K on 38247*2^35500+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.96%
38247*2^35500+1 is prime! (3.5133s+0.0053s)

With all that being said, share some good wholesome prime finds.. hopefully it doesn't die a terrible death again.

kar_bon · 2013-09-20, 08:52

Quote:

Originally Posted by 3.14159

Since the last thread died a slow and terrible death/bumping dead threads = bad forum etiquette..

'Your' Prime posting thread is still here, but without any post for more than 2 years, so it's a few pages down to scroll.

User etiquette should be to read first before insulting.

3.14159 · 2013-09-20, 12:11

To be fair, it's buried somewhere in page 5..

3.14159 · 2013-09-20, 21:31

Searching for a prime that's roughly ~65.5k digits in size. k * 2^217600 + 1, still sieving.

So far I've covered up to ~25.1 trillion. Started off with 300k candidates, now at a little over 11k left, or about 1 in 27. On average, I'm getting rid of one candidate every ~4 minutes (as of the past two hours), testing takes ~4.5 minutes. Should I keep going or do I begin testing now?

In the meantime, friendly bump..
72471*2¹³⁵⁶⁰+1 (4087 digits)
Primality testing 72471*2^13560+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using all-complex FFT length 1K on 72471*2^13560+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.88%
72471*2^13560+1 is prime! (1.5923s+0.0057s)

81253*2¹³⁵⁶⁰+1 (4087 digits)
Primality testing 81253*2^13560+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using all-complex FFT length 1K on 81253*2^13560+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.88%
81253*2^13560+1 is prime! (0.6629s+0.0048s)

speaking of primes, would you look at that.. Posts: 1,657

2011-01-25, 20:24	#917
3.14159 May 2010 Prime hunting commission. 11010010000₂ Posts	Okay.. I haven't submitted anything in a long time.. Here's another prime for you all.. 31240951024194128^3789+1 (7998 digits) Primality testing 31240951024194128^3789+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using generic reduction FFT length 2560 on 31240951024194128^3789+1 Calling Brillhart-Lehmer-Selfridge with factored part 99.84% 31240951024194128^3789+1 is prime! (3.1410s+0.0009s) ≈pi seconds! That's nice. Luckily I have all my prime-searching stuff to continue onwards with. Last fiddled with by 3.14159 on 2011-01-25 at 20:30

2013-09-20, 04:24	#921
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	Prime posting thread, part I lost count.. Since the last thread died a slow and terrible death/bumping dead threads = bad forum etiquette.. Prime posting time to lighten the mood/bring some activity to a semi-dead board/my "home board"? "rules" 1. Anything ≥ 5000 digits is good. In any event, bumping with some kbbs: 577875256⁵²⁵⁶+1 (19561 digits) Running N-1 test using base 5 Special modular reduction using zero-padded AMD K10 type-0 FFT length 12K, Pass1=48, Pass2=256 on 577875256^5256+1 Calling Brillhart-Lehmer-Selfridge with factored part 50.07% 577875256^5256+1 is prime! (33.2498s+0.0184s) 670005256⁵²⁵⁶+1 (19561 digits) Running N-1 test using base 23 Special modular reduction using zero-padded AMD K10 type-0 FFT length 12K, Pass1=48, Pass2=256 on 670005256^5256+1 Calling Brillhart-Lehmer-Selfridge with factored part 50.07% 670005256^5256+1 is prime! (32.7381s+0.0103s) More bumping: 382472³⁵⁵⁰⁰+1 (10692 digits) Primality testing 382472^35500+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using all-complex FFT length 3K on 382472^35500+1 Calling Brillhart-Lehmer-Selfridge with factored part 99.96% 382472^35500+1 is prime! (3.5133s+0.0053s) With all that being said, share some good wholesome prime finds.. hopefully it doesn't die a terrible death again. Last fiddled with by 3.14159 on 2013-09-20 at 04:32

2013-09-20, 21:31	#924
3.14159 May 2010 Prime hunting commission. 690₁₆ Posts	Searching for a prime that's roughly ~65.5k digits in size. k * 2^217600 + 1, still sieving. So far I've covered up to ~25.1 trillion. Started off with 300k candidates, now at a little over 11k left, or about 1 in 27. On average, I'm getting rid of one candidate every ~4 minutes (as of the past two hours), testing takes ~4.5 minutes. Should I keep going or do I begin testing now? In the meantime, friendly bump.. 724712¹³⁵⁶⁰+1 (4087 digits) Primality testing 724712^13560+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using all-complex FFT length 1K on 724712^13560+1 Calling Brillhart-Lehmer-Selfridge with factored part 99.88% 724712^13560+1 is prime! (1.5923s+0.0057s) 812532¹³⁵⁶⁰+1 (4087 digits) Primality testing 812532^13560+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Special modular reduction using all-complex FFT length 1K on 812532^13560+1 Calling Brillhart-Lehmer-Selfridge with factored part 99.88% 812532^13560+1 is prime! (0.6629s+0.0048s) speaking of primes, would you look at that.. Posts: 1,657 Last fiddled with by 3.14159 on 2013-09-20 at 22:00

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2010-12-28, 14:49	#915
lorgix Sep 2010 Scandinavia 267₁₆ Posts	Thanks. The following two are extremely likely to be two-way splits. 17^213+1= ... P74.C129 17^228+1= ... P52.C118 The following two composites have no factors of 30digits or less. 17^222+1= ... P29.C174 17^243+1= ... P34.C133

2011-01-12, 16:50	#916
lorgix Sep 2010 Scandinavia 3·5·41 Posts	I could have sworn I saw this proof this one time... Something about there being an infinite number of primes. Yet this thread is slowing to a stop. Also, in the interest of fairness; we should have a Composite posting thread.

2011-01-25, 21:16	#918
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Another prime for you all; 75622366^4600+1 (8376 digits); Primality testing 75622366^4600+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Special modular reduction using zero-padded FFT length 3584 on 75622366^4600+1 Calling Brillhart-Lehmer-Selfridge with factored part 57.19% 75622366^4600+1 is prime! (1.8654s+0.0274s)

2011-02-02, 04:41	#920
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 41·229 Posts	4*107^32586+1 is a prime and a Generalized Fermat, too

2013-09-20, 12:11	#923
3.14159 May 2010 Prime hunting commission. 2⁴×3×5×7 Posts	To be fair, it's buried somewhere in page 5..