Prime gap records - Page 6

robert44444uk · 2021-12-07, 15:57

Quote:

Originally Posted by MJansen

Hi Seth,

have you been able to add the option to enter large gaps? I have a nice one to add (was hoping for more of course):
5198448 14.335331 363257*363269#/510510-2177806

Kind regards
Michiel

Nice gap! I also gave Seth some 1m+ gaps a while back.

robert44444uk · 2021-12-07, 18:28

Just found a cracking good gap - the highest merit for its size by a substantial margin. It is probably around 21st in merit ever found.

91262 36.934 18453293*2539#/46410-48228

SethTro · 2021-12-07, 22:23

That's a huge find! Congrats! Wish it had been a top 20, still 21st is amazing.

You missed the Dec 6th update so I pushed an extra one just now.

It removes 8 points from the high water mark table! Now there's nothing between my merit 36 gap=78450 and this.

henryzz · 2021-12-14, 12:50

Just submitted a gap I found a while back and never got around to submitting. This is by far my best gap. I think my first record 30 merit as I generally search for larger gaps with lower merit.
105548, C?P, 35.9616, DStevens, 2021-12-14, 1275, 32994233 * 2999#/2303070 -48782

robert44444uk · 2021-12-14, 15:38

Quote:

Originally Posted by henryzz

Just submitted a gap I found a while back and never got around to submitting. This is by far my best gap. I think my first record 30 merit as I generally search for larger gaps with lower merit.
105548, C?P, 35.9616, DStevens, 2021-12-14, 1275, 32994233 * 2999#/2303070 -48782

A handsome find!!

MJansen · 2022-02-22, 21:57

Just now, after PRP-ing for almost 4 weeks after sieving with all primes till 10^12 for 3 1/2 days, the current world record gap between two consecutive probable primes, 6.582.144, has been bested.

The minus side of the gap has been found, the plus side is still going. So the absolute size and merit are unknown as of yet. The gapcenter is at the primorial of the first 40.000 primes, divided by 30030. No additional multiplier was used in the value of the gapcenter.

In common notation, the gap start is at:
479909#/30030 - 3.166.622

The current plus side (still running) is at 3.418.266. This gives a gap of at least 6.584.888 with a merit of 13.743

Will post again when the plus side has been found
Kind regards
Michiel Jansen

rudy235 · 2022-02-23, 00:05

Sounds very interesting! Congrats.

SethTro · 2022-02-23, 06:30

Congrats Michiel! You have always lead the search for megagaps!

robert44444uk · 2022-02-23, 06:55

Ah, a holy grail. It is really hard work to find this type of gap, so massive congrats. I will be only #3 on this list now.

MJansen · 2022-02-25, 09:01

The plus side was found 25-2-2022 at 01.40 UTC/GMT+1 hour.

The search stopped at 479909#/30030 + 3.800.092. Which gives a gap of 6.966.714 at merit 14.540

I have been looking for this record for some time now, started September last year, and I forgot the element of luck needed to find a nice sized gap. Many attempts ended much earlier than hoped for and to give some statistics of this search:

I pre-sieved the interval (together with 7 other intervals) in 3 1/2 days with all primes till 10^12, using Treesieve, a program developed by Jens Kruse Andersen. After that I used Pfgw64 under Ubuntu to PRP the remaining candidate prime values. This took another 32 days and almost 8 hours.

A single PRP at this size of 208.096 digit numbers, took 596 seconds, almost 10 minutes, using a AMD 5900 processor on 12 cores @3500 MHz (leaving 12 threads idle). In the end 35.943 candidate prime numbers were PRP'd. So a single core would have taken 248 days to PRP all candidates.

I have 3 more promising gaps that I will run and after that I will stop the search for another mega gap. Too much of a frustration when the search ends prematurely ;-) But for now happy a new record was set!

Kind regards
Michiel Jansen

ATH · 2022-02-25, 12:53

Congratulations!

Did you save the factors from sieving?

Code:

479909#/30030-3166622+0 is Lucas PRP! (2488.3945s+0.1500s)
479909#/30030-3166622+0 is 31-PRP! (699.4738s+0.1494s)
479909#/30030-3166622+0 is 61-PRP! (698.5678s+0.1491s)
479909#/30030-3166622+0 is 89-PRP! (712.8587s+0.1491s)
479909#/30030-3166622+0 is 107-PRP! (712.6334s+0.1495s)
479909#/30030-3166622+0 is 127-PRP! (699.6641s+0.1507s)

479909#/30030-3166622+6966714 is Lucas PRP! (3137.9045s+0.1848s)
479909#/30030-3166622+6966714 is 31-PRP! (872.6063s+0.1841s)
479909#/30030-3166622+6966714 is 61-PRP! (872.4068s+0.1844s)
479909#/30030-3166622+6966714 is 89-PRP! (872.4274s+0.1843s)
479909#/30030-3166622+6966714 is 107-PRP! (872.6603s+0.1842s)
479909#/30030-3166622+6966714 is 127-PRP! (872.2974s+0.1841s)

2022-02-22, 21:57	#61
MJansen Jan 2018 2×5×11 Posts	New WR - absolute gap between two (probable) primes Just now, after PRP-ing for almost 4 weeks after sieving with all primes till 10^12 for 3 1/2 days, the current world record gap between two consecutive probable primes, 6.582.144, has been bested. The minus side of the gap has been found, the plus side is still going. So the absolute size and merit are unknown as of yet. The gapcenter is at the primorial of the first 40.000 primes, divided by 30030. No additional multiplier was used in the value of the gapcenter. In common notation, the gap start is at: 479909#/30030 - 3.166.622 The current plus side (still running) is at 3.418.266. This gives a gap of at least 6.584.888 with a merit of 13.743 Will post again when the plus side has been found Kind regards Michiel Jansen

2022-02-25, 09:01	#65
MJansen Jan 2018 2×5×11 Posts	Largest absolute gap The plus side was found 25-2-2022 at 01.40 UTC/GMT+1 hour. The search stopped at 479909#/30030 + 3.800.092. Which gives a gap of 6.966.714 at merit 14.540 I have been looking for this record for some time now, started September last year, and I forgot the element of luck needed to find a nice sized gap. Many attempts ended much earlier than hoped for and to give some statistics of this search: I pre-sieved the interval (together with 7 other intervals) in 3 1/2 days with all primes till 10^12, using Treesieve, a program developed by Jens Kruse Andersen. After that I used Pfgw64 under Ubuntu to PRP the remaining candidate prime values. This took another 32 days and almost 8 hours. A single PRP at this size of 208.096 digit numbers, took 596 seconds, almost 10 minutes, using a AMD 5900 processor on 12 cores @3500 MHz (leaving 12 threads idle). In the end 35.943 candidate prime numbers were PRP'd. So a single core would have taken 248 days to PRP all candidates. I have 3 more promising gaps that I will run and after that I will stop the search for another mega gap. Too much of a frustration when the search ends prematurely ;-) But for now happy a new record was set! Kind regards Michiel Jansen

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Prime counting function records	D. B. Staple	Computer Science & Computational Number Theory	50	2020-12-16 07:24
records for primes	3.14159	Information & Answers	8	2018-12-09 00:08
Records for complete factorisation	Brian-E	Math	25	2009-12-16 21:40
gmp-ecm records page question	yqiang	GMP-ECM	6	2007-05-18 12:23
Records in January	wblipp	ElevenSmooth	10	2004-03-22 01:26

2021-12-07, 18:28	#57
robert44444uk Jun 2003 Suva, Fiji 2·1,021 Posts	Just found a cracking good gap - the highest merit for its size by a substantial margin. It is probably around 21st in merit ever found. 91262 36.934 18453293*2539#/46410-48228

2021-12-07, 22:23	#58
SethTro "Seth" Apr 2019 2²·3·41 Posts	That's a huge find! Congrats! Wish it had been a top 20, still 21st is amazing. You missed the Dec 6th update so I pushed an extra one just now. It removes 8 points from the high water mark table! Now there's nothing between my merit 36 gap=78450 and this.

2021-12-14, 12:50	#59
henryzz Just call me Henry "David" Sep 2007 Liverpool (GMT/BST) 5·7·173 Posts	Just submitted a gap I found a while back and never got around to submitting. This is by far my best gap. I think my first record 30 merit as I generally search for larger gaps with lower merit. 105548, C?P, 35.9616, DStevens, 2021-12-14, 1275, 32994233 * 2999#/2303070 -48782

2022-02-23, 00:05	#62
rudy235 Jun 2015 Vallejo, CA/. 3×5×7×11 Posts	Sounds very interesting! Congrats.

2022-02-23, 06:30	#63
SethTro "Seth" Apr 2019 2²×3×41 Posts	Congrats Michiel! You have always lead the search for megagaps!

2022-02-23, 06:55	#64
robert44444uk Jun 2003 Suva, Fiji 7FA₁₆ Posts	Ah, a holy grail. It is really hard work to find this type of gap, so massive congrats. I will be only #3 on this list now.