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Old 2017-07-04, 20:45   #111
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The endpoints are Lucas PRPs and 7- and 11-PRPs.


Code:
Primality testing 499973#/30030-4509212+0 [N+1, Brillhart-Lehmer-Selfridge]
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 720330-bit number                
499973#/30030-4509212+0 is Lucas PRP! (3088.7208s+0.5437s)

Primality testing 499973#/30030-4509212+6582144 [N+1, Brillhart-Lehmer-Selfridge]
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 720330-bit number                
499973#/30030-4509212+6582144 is Lucas PRP! (3101.7580s+0.5407s)

Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330-bit number                
499973#/30030-4509212+0 is 7-PRP! (736.8318s+0.5347s)

Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330-bit number                
499973#/30030-4509212+6582144 is 7-PRP! (736.8739s+0.5383s)

Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330-bit number                
84650698378064473476...12192961872310163557 is 11-PRP! (729.1016s+0.3806s)

Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192 on A 720330-bit number                
84650698378064473476...12192961872316745701 is 11-PRP! (735.1213s+0.3797s)
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Old 2017-07-09, 17:29   #112
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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.
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Old 2017-07-09, 20:40   #113
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Quote:
Originally Posted by ATH View Post
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.
Sorry.
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.
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Old 2017-07-10, 10:52   #114
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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.
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Old 2017-07-13, 14:35   #115
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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.
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Old 2017-07-18, 11:11   #116
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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:

Thank you for sending us the details of the record for 'Largest proven gap between prime numbers'.

Unfortunately, after thoroughly reviewing your application with members of our research team, we are afraid to say that we cannot accept your proposal as a Guinness World Records title.

Our team of expert Records Managers receive thousands of new record proposals every year from all over the world which are carefully assessed to establish if they meet our stringent criteria. Every record verified by Guinness World Records must be measurable by a single superlative, verifiable, standardisable, breakable and also present an element of skill. For our scientific achievement records, we require the achievement to be published in a peer review journal and verified by an independent 3rd party. While I am sure Dr. Thomas R. Nicely can verify your claim we would still need a recognised published paper. As we can understand your disappointment at this time, we would encourage you to apply again when you've met our criteria. All the best
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Old 2017-07-19, 18:06   #117
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Quote:
Originally Posted by robert44444uk View Post
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:
People have asked me if I would show up in the Guinness Book of Records, I told them they most probably wouldn't even care. After all, they could continue with listing the largest known twin primes, or the largest known first occurence gap... I don't think it's of interest to a broad audience. Let alone the fact that the bounding primes are not proven primes.
However, if anyone would be game for writing a "paper", I can give some more details (calculation time etc.)
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Old 2017-08-18, 18:30   #118
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The new gap checked out. All 34,771 pfgw checks were composite:
pfgw0000k-6582k.txt (7 Mb)

Here are the 3,256,300 factors from earlier:
factors.txt
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Old 2017-08-21, 09:36   #119
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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.
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Old 2017-08-21, 12:48   #120
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Well done ATH, and congrats to mart_r - its official!
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