mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2018-03-25, 20:46   #89
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

18210 Posts
Default

I found one for 2^14 and now have:

Code:
(3^(2^0)+1^(2^0))/2
(3^(2^1)+1^(2^1))/2
(3^(2^2)+1^(2^2))/2
(5^(2^3)+3^(2^3))/2
(3^(2^4)+1^(2^4))/2
(3^(2^5)+1^(2^5))/2
(3^(2^6)+1^(2^6))/2
(49^(2^7)+9^(2^7))/2
(7^(2^8)+3^(2^8))/2
(35^(2^9)+9^(2^9))/2
(67^(2^10)+57^(2^10))/2
(49^(2^11)+75^(2^11))/2
(157^(2^12)+83^(2^12))/2
(107^(2^13)+69^(2^13))/2
(71^(2^14)+1^(2^14))/2
Would it be interesting to add this sequence, ..., 35, 67, 49, 157, 107, 71, ..., to OEIS?

/JeppeSN
JeppeSN is offline   Reply With Quote
Old 2018-03-25, 21:17   #90
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

5·1,997 Posts
Default

Yes, why not.
Any sequence is a sequence.
Most of the text can be reused from the previous sequence, and use this sister sequence for the upper boundary https://oeis.org/A275530
Batalov is offline   Reply With Quote
Old 2018-03-26, 09:15   #91
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

18210 Posts
Post

Quote:
Originally Posted by Batalov View Post
Yes, why not.
Any sequence is a sequence.
Most of the text can be reused from the previous sequence, and use this sister sequence for the upper boundary https://oeis.org/A275530
To appear as A301738 (until it is approved, see History to see the proposed versions). /JeppeSN
JeppeSN is offline   Reply With Quote
Old 2018-03-26, 09:44   #92
JeppeSN
 
JeppeSN's Avatar
 
"Jeppe"
Jan 2016
Denmark

101101102 Posts
Lightbulb

We can also restrict ourselves to consecutive odd bases:
\[\frac{a^{2^n}+(a-2)^{2^n}}{2}\]
Can also be parametrized in other ways, such as the \(k\) in:
\[\frac{(2k+1)^{2^n}+(2k-1)^{2^n}}{2}\]
OEIS does not seem to have it either (searching for a, or for a-2, or for 2k=a-1, or for k). /JeppeSN
JeppeSN is offline   Reply With Quote
Old 2018-03-26, 11:02   #93
axn
 
axn's Avatar
 
Jun 2003

34·67 Posts
Default

Quote:
Originally Posted by JeppeSN View Post
We can also restrict ourselves to consecutive odd bases:
\[\frac{a^{2^n}+(a-2)^{2^n}}{2}\]
Can also be parametrized in other ways, such as the \(k\) in:
\[\frac{(2k+1)^{2^n}+(2k-1)^{2^n}}{2}\]
OEIS does not seem to have it either (searching for a, or for a-2, or for 2k=a-1, or for k). /JeppeSN
Code:
(3^2+1^2)/2
(3^4+1^4)/2
(5^8+3^8)/2
(3^16+1^16)/2
(3^32+1^32)/2
(3^64+1^64)/2
(179^128+177^128)/2
(169^256+167^256)/2
(935^512+933^512)/2
(663^1024+661^1024)/2
axn is online now   Reply With Quote
Old 2018-03-26, 13:23   #94
axn
 
axn's Avatar
 
Jun 2003

34·67 Posts
Default

So, I sieved n=17 for 0 < b < a <= 2048 till 2^53. Not sure what range or what depth Serge has sieved on this n, but it looks "sieved enough". This could be used to divide up PRP work.

Quote:
Originally Posted by Batalov View Post
Neat!
...Now time for a quick cuda sieve facelift, based on gfnsieve? ^_^
The logic doesn't exactly correspond to gfn/cyclo sieves, so a cuda sieve will have to be built from scratch, more or less; I have to think about it a bit.
Attached Files
File Type: 7z sieve17.7z (269.7 KB, 75 views)
axn is online now   Reply With Quote
Old 2018-03-26, 16:26   #95
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

609210 Posts
Default

Quote:
Originally Posted by JeppeSN View Post
Would it be interesting to add this sequence, ..., 35, 67, 49, 157, 107, 71, ..., to OEIS?
No. The sequence itself is merely a curiosity. The real interest of this thread, at least for me, has been in the methods described for determining pairs (a, b) for which

a^(2^m) + b^(2^m), [or (a^(2^m) + b^(2^m))/2, if a and b are both odd]

is a (pseudo)prime in a reasonable length of time.
Dr Sardonicus is offline   Reply With Quote
Old 2018-03-26, 21:28   #96
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

5×1,997 Posts
Default

axn's sieve is easily modified for odd-odd pairs. In fact nearly nothing needs to be changed (only the intake parity filters, if they are there; they were in mine, just drop them).
Batalov is offline   Reply With Quote
Old 2018-03-27, 03:02   #97
axn
 
axn's Avatar
 
Jun 2003

34·67 Posts
Default

Quote:
Originally Posted by Batalov View Post
axn's sieve is easily modified for odd-odd pairs. In fact nearly nothing needs to be changed (only the intake parity filters, if they are there; they were in mine, just drop them).
No. The hash matching also needs to change (it currently puts even indexed residues in the hash and uses odd-indexed residues to probe the hash).
axn is online now   Reply With Quote
Old 2018-03-29, 07:23   #98
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

5·1,997 Posts
Exclamation

I am researching a very weird anomaly.

From https://oeis.org/A275530 inquiring minds can find out that a(15) > 10,000.
Or in other words, there are no small prps of the GFN' form (a^32768+1)/2.

Now, from what I checked with PFGW, a(15) appears to be either > 160,000 (or even >200,000, which is unreasonably high), or there is a bug in libgwnum. I checked with pfgw, llr, p95 but the speed and results are similar (and the underlying lib is the same). All programs chose the special FFT of size 32K. Changing FFT size to a larger one doesn't help to find a PRP yet. Very strange.
Batalov is offline   Reply With Quote
Old 2018-03-29, 08:25   #99
axn
 
axn's Avatar
 
Jun 2003

10101001100112 Posts
Default

Quote:
Originally Posted by Batalov View Post
I am researching a very weird anomaly.

From https://oeis.org/A275530 inquiring minds can find out that a(15) > 10,000.
Or in other words, there are no small prps of the GFN' form (a^32768+1)/2.

Now, from what I checked with PFGW, a(15) appears to be either > 160,000 (or even >200,000, which is unreasonably high), or there is a bug in libgwnum. I checked with pfgw, llr, p95 but the speed and results are similar (and the underlying lib is the same). All programs chose the special FFT of size 32K. Changing FFT size to a larger one doesn't help to find a PRP yet. Very strange.
Well, the main one (http://oeis.org/A226530) has first three as 70906, 167176, 204462. So > 200k, while low probability, is not _that_ unexpected.
axn is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Is there a prime of the form...... PawnProver44 Miscellaneous Math 9 2016-03-19 22:11
OEIS A071580: Smallest prime of the form k*a(n-1)*a(n-2)*...*a(1)+1 arbooker And now for something completely different 14 2015-05-22 23:18
Smallest prime with a digit sum of 911 Stargate38 Puzzles 6 2014-09-29 14:18
Smallest floor of k for cullen prime Citrix Prime Cullen Prime 12 2007-04-26 19:52
Smallest ten-million-digit prime Heck Factoring 9 2004-10-28 11:34

All times are UTC. The time now is 15:15.


Sun Nov 27 15:15:30 UTC 2022 up 101 days, 12:44, 1 user, load averages: 1.36, 1.08, 1.02

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, 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