20170704, 20:45  #111 
Einyen
Dec 2003
Denmark
2^{2}×3^{3}×31 Posts 
The endpoints are Lucas PRPs and 7 and 11PRPs.
Code:
Primality testing 499973#/300304509212+0 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 2, base 2+sqrt(2) Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330bit number 499973#/300304509212+0 is Lucas PRP! (3088.7208s+0.5437s) Primality testing 499973#/300304509212+6582144 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 2, base 2+sqrt(2) Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330bit number 499973#/300304509212+6582144 is Lucas PRP! (3101.7580s+0.5407s) Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330bit number 499973#/300304509212+0 is 7PRP! (736.8318s+0.5347s) Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330bit number 499973#/300304509212+6582144 is 7PRP! (736.8739s+0.5383s) Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330bit number 84650698378064473476...12192961872310163557 is 11PRP! (729.1016s+0.3806s) Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330bit number 84650698378064473476...12192961872316745701 is 11PRP! (735.1213s+0.3797s) 
20170709, 17:29  #112 
Einyen
Dec 2003
Denmark
2^{2}·3^{3}·31 Posts 
In the future when you guys are looking for record big gaps maybe you can save the factors you find during the run??
It would save a lot of time in the verification not having to trial factor all over again instead of just test dividing the saved factors. 
20170709, 20:40  #113  
Dec 2008
you know...around...
19·41 Posts 
Quote:
But my sieve didn't go very deep anyway, only to 2^32. I know that's far from optimal, but I also consider it a bit more safe. 

20170710, 10:52  #114 
Jun 2003
Suva, Fiji
11111110111_{2} Posts 
By the way, the Guinness World Records is looking into prime gaps as a new category for its book and website. I'm handling that enquiry at present.

20170713, 14:35  #115 
Einyen
Dec 2003
Denmark
2^{2}·3^{3}·31 Posts 
I trial factored Martin's range up to 675G and found 3,256,300 factors. First column is distance from the lowest prime and second column is the factor.
factors.txt That leaves 34,771 candidates: candidates.txt I have started checking with pfgw on the first 18,834 below 2M from the lowest prime, if anyone else wants to help double checking. I'm using the l switch to save a log from pfgw. 
20170718, 11:11  #116  
Jun 2003
Suva, Fiji
2,039 Posts 
I have now heard from the Guinness Book of Records  not good news I am afraid, although there is time in the next year to rectify shortcomings:
Quote:


20170719, 18:06  #117  
Dec 2008
you know...around...
19×41 Posts 
Quote:
However, if anyone would be game for writing a "paper", I can give some more details (calculation time etc.) 

20170818, 18:30  #118 
Einyen
Dec 2003
Denmark
2^{2}×3^{3}×31 Posts 
The new gap checked out. All 34,771 pfgw checks were composite:
pfgw0000k6582k.txt (7 Mb) Here are the 3,256,300 factors from earlier: factors.txt 
20170821, 09:36  #119 
Dec 2008
you know...around...
19·41 Posts 
Thank you so much ATH!
I expected the doublecheck to take at least two months, so I'm quite amazed that you did it all in half the time. I've sent the confirmation to Dr. Nicely. 
20170821, 12:48  #120 
Jun 2003
Suva, Fiji
2,039 Posts 
Well done ATH, and congrats to mart_r  its official!

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