20101228, 14:08  #914 
"William"
May 2003
New Haven
4471_{8} Posts 
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 
20101228, 14:49  #915 
Sep 2010
Scandinavia
267_{16} Posts 
Thanks.
The following two are extremely likely to be twoway 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 
20110112, 16:50  #916 
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. 
20110125, 20:24  #917 
May 2010
Prime hunting commission.
11010010000_{2} Posts 
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 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 Special modular reduction using generic reduction FFT length 2560 on 31240951024194*128^3789+1 Calling BrillhartLehmerSelfridge 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 primesearching stuff to continue onwards with. Last fiddled with by 3.14159 on 20110125 at 20:30 
20110125, 21:16  #918 
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
Another prime for you all;
756223*66^4600+1 (8376 digits); Primality testing 756223*66^4600+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 19 Special modular reduction using zeropadded FFT length 3584 on 756223*66^4600+1 Calling BrillhartLehmerSelfridge with factored part 57.19% 756223*66^4600+1 is prime! (1.8654s+0.0274s) 
20110131, 17:34  #919 
May 2010
Prime hunting commission.
2^{4}×3×5×7 Posts 
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 Last fiddled with by 3.14159 on 20110131 at 17:48 
20110202, 04:41  #920 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41·229 Posts 
4*107^32586+1 is a prime and a Generalized Fermat, too

20130920, 04:24  #921 
May 2010
Prime hunting commission.
2^{4}×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 semidead board/my "home board"? "rules" 1. Anything ≥ 5000 digits is good. In any event, bumping with some kbbs: 57787*5256^{5256}+1 (19561 digits) Running N1 test using base 5 Special modular reduction using zeropadded AMD K10 type0 FFT length 12K, Pass1=48, Pass2=256 on 57787*5256^5256+1 Calling BrillhartLehmerSelfridge with factored part 50.07% 57787*5256^5256+1 is prime! (33.2498s+0.0184s) 67000*5256^{5256}+1 (19561 digits) Running N1 test using base 23 Special modular reduction using zeropadded AMD K10 type0 FFT length 12K, Pass1=48, Pass2=256 on 67000*5256^5256+1 Calling BrillhartLehmerSelfridge with factored part 50.07% 67000*5256^5256+1 is prime! (32.7381s+0.0103s) More bumping: 38247*2^{35500}+1 (10692 digits) Primality testing 38247*2^35500+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 Special modular reduction using allcomplex FFT length 3K on 38247*2^35500+1 Calling BrillhartLehmerSelfridge 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. Last fiddled with by 3.14159 on 20130920 at 04:32 
20130920, 08:52  #922  
Mar 2006
Germany
2881_{10} Posts 
Quote:
User etiquette should be to read first before insulting. 

20130920, 12:11  #923 
May 2010
Prime hunting commission.
2^{4}×3×5×7 Posts 
To be fair, it's buried somewhere in page 5..

20130920, 21:31  #924 
May 2010
Prime hunting commission.
690_{16} 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.. 72471*2^{13560}+1 (4087 digits) Primality testing 72471*2^13560+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 5 Special modular reduction using allcomplex FFT length 1K on 72471*2^13560+1 Calling BrillhartLehmerSelfridge with factored part 99.88% 72471*2^13560+1 is prime! (1.5923s+0.0057s) 81253*2^{13560}+1 (4087 digits) Primality testing 81253*2^13560+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 3 Special modular reduction using allcomplex FFT length 1K on 81253*2^13560+1 Calling BrillhartLehmerSelfridge 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 Last fiddled with by 3.14159 on 20130920 at 22:00 
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