Prime gap records - Page 9

Bobby Jacobs · 2022-04-17, 17:21

Wow! Another record already? That is amazing. Congratulations!

ATH · 2022-04-17, 18:18

Quote:

Originally Posted by MJansen

The gap of primorial 29*479909#/9699690 is 7186572, with 208095 digits and merit 14.998450.
The gap has end points:
29*479909#/9699690-3531714
and
29*479909#/9699690+3654858

Code:

29*479909#/9699690-3531714+0 is 2-PRP! (1377.0026s+0.2389s)
29*479909#/9699690-3531714+0 is 31-PRP! (1406.6504s+0.2672s)
29*479909#/9699690-3531714+0 is 61-PRP! (1324.6448s+0.3519s)
29*479909#/9699690-3531714+0 is 89-PRP! (1351.6884s+0.1892s)
29*479909#/9699690-3531714+0 is 107-PRP! (1337.2569s+0.2194s)
29*479909#/9699690-3531714+0 is 127-PRP! (1295.6427s+0.2666s)
29*479909#/9699690-3531714+0 is Lucas PRP! (5028.9635s+0.3283s)

29*479909#/9699690-3531714+7186572 is 2-PRP! (1398.9850s+0.2509s)
29*479909#/9699690-3531714+7186572 is 31-PRP! (1325.3246s+0.2589s)
29*479909#/9699690-3531714+7186572 is 61-PRP! (1257.9103s+0.2403s)
29*479909#/9699690-3531714+7186572 is 89-PRP! (1253.9708s+0.2486s)
29*479909#/9699690-3531714+7186572 is 107-PRP! (1253.6129s+0.1967s)
29*479909#/9699690-3531714+7186572 is 127-PRP! (1316.4862s+0.3536s)
29*479909#/9699690-3531714+7186572 is Lucas PRP! (6843.9628s+0.2712s)

Congratulations again on another record.

Sorry, I'm not going to double check this gap just after finishing the other one.

In the future I think it would be beneficial to start the sieving longer time before you want to use all the cores on the PRP tests and then let sieving run longer. Each PRP test takes 10-20 min on 1 core depending on the CPU, and I'm pretty sure sieving finds more than 6 factors per hour after 1e12, it is probably beneficial to 2e12 or even longer.
Since the sieving is single threaded it is just a matter of starting it on 1 core like 1-2 weeks before you want to use lots of cores for all the PRP tests.

robert44444uk · 2022-04-18, 00:51

Quote:

Originally Posted by MJansen

Sounds interesting Robert! What country if I may ask?
PS my last search is currently 5th and close to 4th with both endpoints still to be found. High hopes here as well ;-)

Kind regards
Michiel

I'm in Australia at present, awaiting my partners work visa application for Fiji. I'll be in Fiji for 2 years. I won't have my 16 core machine sadly, it would not cope with the heat and humidity. I'm hoping my old 8 core will, but it needs to be shipped, and won't be with me for a couple of months at a minimum.

MJansen · 2022-04-18, 20:12

Quote:

Originally Posted by Bobby Jacobs

Wow! Another record already? That is amazing. Congratulations!

Thnx Bobby! Mostly luck though

Kind regards
Michiel

MJansen · 2022-04-18, 20:55

Quote:

Originally Posted by ATH

Code:

29*479909#/9699690-3531714+0 is 2-PRP! (1377.0026s+0.2389s)
29*479909#/9699690-3531714+0 is 31-PRP! (1406.6504s+0.2672s)
29*479909#/9699690-3531714+0 is 61-PRP! (1324.6448s+0.3519s)
29*479909#/9699690-3531714+0 is 89-PRP! (1351.6884s+0.1892s)
29*479909#/9699690-3531714+0 is 107-PRP! (1337.2569s+0.2194s)
29*479909#/9699690-3531714+0 is 127-PRP! (1295.6427s+0.2666s)
29*479909#/9699690-3531714+0 is Lucas PRP! (5028.9635s+0.3283s)

29*479909#/9699690-3531714+7186572 is 2-PRP! (1398.9850s+0.2509s)
29*479909#/9699690-3531714+7186572 is 31-PRP! (1325.3246s+0.2589s)
29*479909#/9699690-3531714+7186572 is 61-PRP! (1257.9103s+0.2403s)
29*479909#/9699690-3531714+7186572 is 89-PRP! (1253.9708s+0.2486s)
29*479909#/9699690-3531714+7186572 is 107-PRP! (1253.6129s+0.1967s)
29*479909#/9699690-3531714+7186572 is 127-PRP! (1316.4862s+0.3536s)
29*479909#/9699690-3531714+7186572 is Lucas PRP! (6843.9628s+0.2712s)

Congratulations again on another record.

Sorry, I'm not going to double check this gap just after finishing the other one.

In the future I think it would be beneficial to start the sieving longer time before you want to use all the cores on the PRP tests and then let sieving run longer. Each PRP test takes 10-20 min on 1 core depending on the CPU, and I'm pretty sure sieving finds more than 6 factors per hour after 1e12, it is probably beneficial to 2e12 or even longer.
Since the sieving is single threaded it is just a matter of starting it on 1 core like 1-2 weeks before you want to use lots of cores for all the PRP tests.

Thnx Andreas! No worries about not running the gap again, the classification should at least be PRP after you verified the gap ends.

I did sieve multiple gaps before I started PRP-ing them. After that I PRP-d 6 different gaps for 2 weeks and the ones that did not had any end points found, I searched seperately later, among this one.

I did not sieve the interval further because of the dimininishing returns, i.e. the number of composites found decreased fairly fast already, not sure how much sieving till 2*10^12 would save ...
After 70*10^10 the number of (new) composites that is found is around 0,0006% (6/1.000.000th) of the total candidates. Say 162 candidates for the primes between 69-70 * 10^10, in an interval of 25.306.551 candidates for a primorial of the first 42.000 primes. So extending the presieving till 10^12 is already a bit superfluous imho, doubling that till 2*10^12 seems excessive at the moment, but if (big if!) I will do another mega gap search I will keep this in mind.

This record can be improved very easily if :
a. there is a bignum library for the GPU
b. a gpu is used for sieving and PRP-ing. If for instance the speed of a GPU core is half that of a cpu core, the number of available cores (1.000 - 10.000+) makes that job so much easier ...

Note I still have not been able to get the GPU to run a gap search, I installed the necessairy programs under Ubuntu, but for the life of me I do not know how to tell the gapsearch program where they can be found ...

MJansen · 2022-04-18, 20:57

Quote:

Originally Posted by robert44444uk

I'm in Australia at present, awaiting my partners work visa application for Fiji. I'll be in Fiji for 2 years. I won't have my 16 core machine sadly, it would not cope with the heat and humidity. I'm hoping my old 8 core will, but it needs to be shipped, and won't be with me for a couple of months at a minimum.

Wow, cool! Seems like a brilliant adventure, enjoy!
Forgive me the question, but I am curious: How did your mega gap turn out? Still running?

Kind regards
Michiel

mart_r · 2022-04-19, 16:35

I could donate some cycles for PRPing (four OpenPFGW instances, each can check one number in about 13 minutes, ballpark).
Provided that someone else can do the sieving part. Or is a list of divisors > 10^10 (say) available, so I can sieve for the small factors myself and then take the numbers from that list?

robert44444uk · 2022-04-20, 00:53

Quote:

Originally Posted by MJansen

Wow, cool! Seems like a brilliant adventure, enjoy!
Forgive me the question, but I am curious: How did your mega gap turn out? Still running?

Kind regards
Michiel

It's on hold until I have a machine shipped out. I do have the files for the candidate if anyone wants to share the number. I have pfgw files for 4 separate pfgw instances/ consoles - when run in parallel it means that it is relatively efficient where no end points have been found. But you do have to run all 4. I never did figure out how to use pfgw threaded.

I'm only checking this forum about once a week at the mo. Too much going on!

robert44444uk · 2022-04-20, 00:54

Quote:

Originally Posted by mart_r

I could donate some cycles for PRPing (four OpenPFGW instances, each can check one number in about 13 minutes, ballpark).
Provided that someone else can do the sieving part. Or is a list of divisors > 10^10 (say) available, so I can sieve for the small factors myself and then take the numbers from that list?

The number is already sieved up to 1e12

MJansen · 2022-04-20, 05:55

Quote:

Originally Posted by robert44444uk

It's on hold until I have a machine shipped out. I do have the files for the candidate if anyone wants to share the number. I have pfgw files for 4 separate pfgw instances/ consoles - when run in parallel it means that it is relatively efficient where no end points have been found. But you do have to run all 4. I never did figure out how to use pfgw threaded.

I'm only checking this forum about once a week at the mo. Too much going on!

I would be willing to do that, I will run the remaining candidates on 12 cores if you can let me know how far each of the 4 files has progressed. Send me a PM for the details.

Kind regards
Michiel

MJansen · 2022-04-20, 06:01

Quote:

Originally Posted by mart_r

I could donate some cycles for PRPing (four OpenPFGW instances, each can check one number in about 13 minutes, ballpark).
Provided that someone else can do the sieving part. Or is a list of divisors > 10^10 (say) available, so I can sieve for the small factors myself and then take the numbers from that list?

That would be great, I have the files with the candidates (sieved till 10^12) if you want, but be aware: it might take you 6000 hours in total, 1500 when using 4 cores. That means 62,5 days ...

Maybe we can work out a smarter way? Doeing a sample check?
I think the -a1 option of Pfgw also saves the outcome of a PRP, not sure, but maybe than we can spread the effort?

Open for suggestions
Kind regards
Michiel

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2022-04-17, 17:21	#89
Bobby Jacobs May 2018 2·11·13 Posts	Wow! Another record already? That is amazing. Congratulations!

2022-04-19, 16:35	#95
mart_r Dec 2008 you know...around... 2³·109 Posts	I could donate some cycles for PRPing (four OpenPFGW instances, each can check one number in about 13 minutes, ballpark). Provided that someone else can do the sieving part. Or is a list of divisors > 10^10 (say) available, so I can sieve for the small factors myself and then take the numbers from that list?