mersenneforum.org New Maximal Gaps
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

2021-07-28, 08:53   #34
SethTro

"Seth"
Apr 2019

1ED16 Posts

Quote:
 Originally Posted by rudy235 i looked for it at the prime gap tables and it was not there. Did you report it?
That's on me, the primegap github site is updated manually ~monthly. I updated it today. 1572 now appears on https://primegap-list-project.github...gh-watermarks/

 2021-08-01, 17:45 #35 Bobby Jacobs     May 2018 4458 Posts Have the new gaps of 1552 and 1572 been confirmed as maximal prime gaps yet? How close are you to confirming them?
 2021-08-19, 18:37 #36 CraigLo   Mar 2021 59 Posts I don't think anyone is working on confirming them. My code can't be used for confirmation. I don't have much CPU resources to contribute and I'm not sure what code others have used. I might be able to help speed up some of the existing CPU code.
 2021-08-19, 19:00 #37 CraigLo   Mar 2021 59 Posts I've checked up to 264 + 61*1016. In addition to the 1552 and 1572 I found 7 gaps in the 1400s but the largest is still 1430 so no new first occurrences.
 2021-08-23, 15:50 #38 Bobby Jacobs     May 2018 293 Posts I thought you started at 264 and worked continuously from there. How are you not sure that these are maximal prime gaps? Did you skip any primes?
2021-08-23, 19:14   #39
rudy235

Jun 2015
Vallejo, CA/.

33×43 Posts

Quote:
 I reached 264 + 1.05*1016 = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 264 + 2.33*1016 so I'm not even half way.
ATH

This is the status of the exhaustive search. (Unless someone else has covered the numbers after 264+1.03 x1016)

To check in a reliable way that no gap greater or equal to 1432 exists below 264 +2.33x1016where the gap of 1552 is found is a gruesome task as we no longer have the support of the code that allowed us to reach 264-232.

As things stand now the smallest gap that we don’t know with certainty to be a “first occurrence” is 1432.

 2021-08-24, 14:01 #40 CraigLo   Mar 2021 3B16 Posts I checked continuously from 264 but I'm only doing 1 Fermat test so it is possible that a number is incorrectly called a prime. I think it is unlikely that this has lead to missing a large gap (very unlikely if the math in this post is correct https://mersenneforum.org/showpost.p...8&postcount=20) but it is still possible. The easiest way for me to fix this issue would be to use 12 SPRP tests which is sufficient to prove primality. Half the remaining numbers are prime after sieving so the code would take about 6-7 times longer to run. It's possible it would be faster to check with sieving only. It would require sieving up to primes a little above 232. This is also new GPU code so it is possible that there is some other error. I did find all the gaps above 1000 that ATH found so there is some confidence that it is working correctly.
2021-08-24, 15:56   #41
ATH
Einyen

Dec 2003
Denmark

2·3·52·23 Posts

Quote:
 Originally Posted by CraigLo The easiest way for me to fix this issue would be to use 12 SPRP tests which is sufficient to prove primality. Half the remaining numbers are prime after sieving so the code would take about 6-7 times longer to run.
It would be faster with 1 SPRP + 1 Lucas than 12 SPRP. At least the CPU code with the GMP library 1 Lucas test is about equal to 6.4-6.6 SPRP tests at 264 + 2*1016.
Why does 12 SPRP tests prove primality?

2021-08-24, 17:06   #42
rudy235

Jun 2015
Vallejo, CA/.

33×43 Posts

Quote:
 Originally Posted by ATH Why does 12 SPRP tests prove primality?
I was wondering exactly the same thing. On the other hand, a number of the order of 10^19 can be proven prime easily by trial division or sieving.

Keeking track of the Numbers that STILL have not yet been established as a First Occurrence Gap. (The last one 1552 is most probably a first occurrence and thus a Maximal Gap)
• 1432
• 1444
• 1458
• 1472
• 1474
• 1478
• 1480
• 1484
• 1492
• 1496
• 1498
• 1500
• 1504
• 1508
• 1512
• 1514
• 1516
• 1518
• 1520
• 1522
• 1524
• 1528
• 1532
• 1534
• 1536
• 1538
• 1540
• 1542
• 1544
• 1546
• 1548
• 1552

I am assuming none of these numbers, with the exception of 1552, have been improved since November 2019

Last fiddled with by rudy235 on 2021-08-24 at 17:08

 2021-08-24, 18:32 #43 CraigLo   Mar 2021 59 Posts Bases of 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37 have been proven a deterministic test up to 3.18 * 1023. https://en.wikipedia.org/wiki/Miller...primality_test For 265 this can likely be reduced to 7 or better but I don't think it has been proven beyond 264. https://miller-rabin.appspot.com/
 2021-08-24, 20:45 #44 CraigLo   Mar 2021 1110112 Posts There is a list of base 2 pseudoprimes up to 264. http://www.janfeitsma.nl/math/psp2/index When you guys were doing the search up to 264 it would have been faster to do the Lucas test only if the number was a known 2-PSP. Unfortunately the list only goes up to 264. Is there a fast way to generate the list of 2-PSP. When checking for gaps we need to do one Lucas test for every 1400 numbers. To check from 264 to 264 + 2.33 * 1016 (Gap=1552) would require 1.66*1013 Lucas tests. Can the list of 2-PSP be computed faster than this? We wouldn't even need to rerun what has already been done. We could just check for large gaps around the 2-PSPs.

 Similar Threads Thread Thread Starter Forum Replies Last Post Bobby Jacobs Prime Gap Searches 7 2022-08-28 12:12 Bobby Jacobs Prime Gap Searches 52 2020-08-22 15:20 Bobby Jacobs Prime Gap Searches 5 2019-03-17 20:01 robert44444uk Prime Gap Searches 1 2018-07-10 20:50 gd_barnes Riesel Prime Search 11 2007-06-27 04:12

All times are UTC. The time now is 01:48.

Sun Jun 4 01:48:36 UTC 2023 up 289 days, 23:17, 0 users, load averages: 1.10, 0.97, 0.88

Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔