mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 440
Search took 0.07 seconds.
Search: Posts Made By: Dobri
Forum: Miscellaneous Math 2022-11-30, 04:41
Replies: 619
Views: 95,972
Posted By Dobri
Roger that, Boss-168. :tu:

Roger that, Boss-168. :tu:
Forum: Dobri 2022-11-28, 12:49
Replies: 84
Views: 42,246
Posted By Dobri
Indeed, the letter 'n' in the file names of the...

Indeed, the letter 'n' in the file names of the attachments to post #73 is used instead of the minus sign '-':
MpLCSUlamX5973Yn2658D1500b28.txt (for y = -2658) and
MpLCSUlamXn5973Y2658D1500b28.txt...
Forum: Dobri 2022-11-28, 09:05
Replies: 84
Views: 42,246
Posted By Dobri
At the intersection in the Venn diagram of three...

At the intersection in the Venn diagram of three discrete sets obtained with:

- longest common subsequences (LCS);
- Ulam clockwise square spiral (UCS); and
- binary substring elimination...
Forum: Dobri 2022-11-28, 07:51
Replies: 84
Views: 42,246
Posted By Dobri
Here are all 216 9-bit binary strings that cannot...

Here are all 216 9-bit binary strings that cannot be found as sub-strings in any of the prime exponents of known Mersenne primes.

Nine-bit strings:
000000100
000001000
000001010
000001110...
Forum: Dobri 2022-11-25, 01:28
Replies: 84
Views: 42,246
Posted By Dobri
Here are the shortest binary strings that cannot...

Here are the shortest binary strings that cannot be found as sub-strings in any of the 51 exponents of known Mersenne primes.

Seven-bit strings:
0001000
1110010

Eight-bit strings:
00001000...
Forum: Dobri 2022-11-25, 01:06
Replies: 84
Views: 42,246
Posted By Dobri
I will post updates occasionally indeed but in...

I will post updates occasionally indeed but in new posts without editing old ones, like in the example below.
Forum: Miscellaneous Math 2022-11-22, 06:50
Replies: 619
Views: 95,972
Posted By Dobri
Both are currently progressing on devices...

Both are currently progressing on devices disconnected from the network.
Forum: Dobri 2022-11-22, 06:34
Replies: 84
Views: 42,246
Posted By Dobri
The curves of the sorted arrays of ln(|x-y|) and...

The curves of the sorted arrays of ln(|x-y|) and ln(|x|+|y|) of the x-y coordinates of the prime exponents of known Mersenne primes on a modified Ulam clockwise square spiral of ๐œ‹(p) are shown in the...
Forum: Dobri 2022-11-17, 01:01
Replies: 84
Views: 42,246
Posted By Dobri
In addition to the linear tendency of the sorted...

In addition to the linear tendency of the sorted array of ln(|x-y|) of the x-y coordinates of the prime exponents of known Mersenne primes on a modified Ulam clockwise square spiral of ๐œ‹(p) in post...
Forum: Dobri 2022-11-11, 20:11
Replies: 84
Views: 42,246
Posted By Dobri
This is a correction of an apparent typo in the...

This is a correction of an apparent typo in the previous post. The correction replaces a positive sign with a negative sign as follows:
sgn(x) elinear term 1 - sgn(y) elinear term 2 = sgn(x-y)...
Forum: Dobri 2022-11-11, 17:41
Replies: 84
Views: 42,246
Posted By Dobri
The assumed linear tendencies of sorted arrays of...

The assumed linear tendencies of sorted arrays of ln(|x|), ln(|y|), and ln(|x-y|) correspond to an equation for which there is no known analytical solution:

sgn(x) elinear term 1 + sgn(y) elinear...
Forum: Dobri 2022-11-11, 07:42
Replies: 84
Views: 42,246
Posted By Dobri
The linear tendency of the sorted array of...

The linear tendency of the sorted array of Log[Abs[x-y]] of the x-y coordinates of the prime exponents of known Mersenne primes is preserved also on a modified Ulam clockwise square spiral of ๐œ‹(p)...
Forum: Dobri 2022-11-07, 19:23
Replies: 84
Views: 42,246
Posted By Dobri
Let โˆ†x = โˆ†y = 1500. Then the intersection subset...

Let โˆ†x = โˆ†y = 1500. Then the intersection subset between the LCS-generated and UCS-generated sets around each central point contains several hundred 28-bit prime exponents to be tested for the first...
Forum: Dobri 2022-11-04, 08:42
Replies: 84
Views: 42,246
Posted By Dobri
The 28-bit LCS-generated set in post #40 is...

The 28-bit LCS-generated set in post #40 is obtained without the use of bit reversal and cyclic folding operations.

Using a larger LCS set involving said operations and also a larger UCS set (by...
Forum: Dobri 2022-11-04, 06:03
Replies: 84
Views: 42,246
Posted By Dobri
For completeness, here is the code used to obtain...

For completeness, here is the code used to obtain the linear fit of Log[Abs[x-y]] in post #68, https://mersenneforum.org/showpost.php?p=617057&postcount=68.

(* Wolfram code *)...
Forum: Dobri 2022-11-04, 05:20
Replies: 84
Views: 42,246
Posted By Dobri
Let's consider the intersection between...

Let's consider the intersection between LCS-generated sets and Ulam-clockwise-square-spiral-(UCS)-generated sets.

The intersections between the 28-bit LCS set in post #40,...
Forum: Dobri 2022-11-03, 20:38
Replies: 84
Views: 42,246
Posted By Dobri
The prime with coordinates closest to x โ‰ˆ 5973...

The prime with coordinates closest to x โ‰ˆ 5973 and y โ‰ˆ -2658 is M142691651 (Untested) with x = 5973 and y = -2654.

The prime with coordinates closest to x โ‰ˆ -5973 and y โ‰ˆ 2658 is M142715557...
Forum: Dobri 2022-11-03, 13:06
Replies: 84
Views: 42,246
Posted By Dobri
Assuming a linear tendency for the approximation...

Assuming a linear tendency for the approximation of Log[Abs[x-y]] of the coordinates x and y of the prime exponent of the next Mersenne prime M52 (if any) in Ulam clockwise square spiral, a...
Forum: Dobri 2022-10-31, 22:16
Replies: 84
Views: 42,246
Posted By Dobri
Assuming a linear tendency for the approximation...

Assuming a linear tendency for the approximation of Log[Abs[x]] and Log[Abs[y]] of the coordinates x and y of the prime exponent of the next Mersenne prime (if any) in Ulam clockwise square spiral, a...
Forum: Lounge 2022-10-31, 18:28
Replies: 4,522
Views: 467,513
Posted By Dobri
After displaying the web page in the Chromium...

After displaying the web page in the Chromium browser, my Raspberry Pi 4B device (connected to a 4K TV set) freezes completely too.
Forum: Dobri 2022-10-31, 12:25
Replies: 84
Views: 42,246
Posted By Dobri
The attached graph shows the sorted list of...

The attached graph shows the sorted list of Log[Abs[x]] and Log[Abs[y]] values of x- and y-coordinates of the prime exponents of known Mersenne primes in Ulam clockwise square spiral.
...
Forum: Dobri 2022-10-31, 05:03
Replies: 84
Views: 42,246
Posted By Dobri
List of x-coordinates of the prime exponents of...

List of x-coordinates of the prime exponents of known Mersenne primes in Ulam clockwise square spiral (see also OEIS A174344):
...
Forum: Dobri 2022-10-29, 08:07
Replies: 84
Views: 42,246
Posted By Dobri
The presence of {0,2-1/2,0,0, 2-1/2} is due to...

The presence of {0,2-1/2,0,0, 2-1/2} is due to M1279,
the presence of {(2/3)1/2,-6-1/2,0,0, 6-1/2} is due to M2203, and
the presence of {3-1/2,3-1/2,0,0,-3-1/2} is due to M3217,
Forum: Dobri 2022-10-28, 18:02
Replies: 84
Views: 42,246
Posted By Dobri
Obviously, the determinant of the 3ร—3 matrix {{0,...

Obviously, the determinant of the 3ร—3 matrix {{0, 1/Sqrt[2], 1/Sqrt[2]}, {Sqrt[2/3], -(1/Sqrt[6]), 1/Sqrt[6]}, {1/Sqrt[3], 1/Sqrt[3], -1/Sqrt[3]}} is equal to 1.

See some of the properties of said...
Forum: Dobri 2022-10-28, 16:44
Replies: 84
Views: 42,246
Posted By Dobri
Let's represent the 51 prime exponents of known...

Let's represent the 51 prime exponents of known Mersenne primes as 27-bit binary strings:
...
Showing results 1 to 25 of 440

 
All times are UTC. The time now is 05:08.


Mon Dec 5 05:08:57 UTC 2022 up 109 days, 2:37, 0 users, load averages: 1.13, 1.19, 1.13

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.

โ‰  ยฑ โˆ“ รท ร— ยท โˆ’ โˆš โ€ฐ โŠ— โŠ• โŠ– โŠ˜ โŠ™ โ‰ค โ‰ฅ โ‰ฆ โ‰ง โ‰จ โ‰ฉ โ‰บ โ‰ป โ‰ผ โ‰ฝ โŠ โŠ โŠ‘ โŠ’ ยฒ ยณ ยฐ
โˆ  โˆŸ ยฐ โ‰… ~ โ€– โŸ‚ โซ›
โ‰ก โ‰œ โ‰ˆ โˆ โˆž โ‰ช โ‰ซ โŒŠโŒ‹ โŒˆโŒ‰ โˆ˜ โˆ โˆ โˆ‘ โˆง โˆจ โˆฉ โˆช โจ€ โŠ• โŠ— ๐–• ๐–– ๐–— โŠฒ โŠณ
โˆ… โˆ– โˆ โ†ฆ โ†ฃ โˆฉ โˆช โŠ† โŠ‚ โŠ„ โŠŠ โŠ‡ โŠƒ โŠ… โŠ‹ โŠ– โˆˆ โˆ‰ โˆ‹ โˆŒ โ„• โ„ค โ„š โ„ โ„‚ โ„ต โ„ถ โ„ท โ„ธ ๐“Ÿ
ยฌ โˆจ โˆง โŠ• โ†’ โ† โ‡’ โ‡ โ‡” โˆ€ โˆƒ โˆ„ โˆด โˆต โŠค โŠฅ โŠข โŠจ โซค โŠฃ โ€ฆ โ‹ฏ โ‹ฎ โ‹ฐ โ‹ฑ
โˆซ โˆฌ โˆญ โˆฎ โˆฏ โˆฐ โˆ‡ โˆ† ฮด โˆ‚ โ„ฑ โ„’ โ„“
๐›ข๐›ผ ๐›ฃ๐›ฝ ๐›ค๐›พ ๐›ฅ๐›ฟ ๐›ฆ๐œ€๐œ– ๐›ง๐œ ๐›จ๐œ‚ ๐›ฉ๐œƒ๐œ— ๐›ช๐œ„ ๐›ซ๐œ… ๐›ฌ๐œ† ๐›ญ๐œ‡ ๐›ฎ๐œˆ ๐›ฏ๐œ‰ ๐›ฐ๐œŠ ๐›ฑ๐œ‹ ๐›ฒ๐œŒ ๐›ด๐œŽ๐œ ๐›ต๐œ ๐›ถ๐œ ๐›ท๐œ™๐œ‘ ๐›ธ๐œ’ ๐›น๐œ“ ๐›บ๐œ”