mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 317
Search took 0.05 seconds.
Search: Posts Made By: Dobri
Forum: Dobri 2022-05-18, 14:56
Replies: 53
Views: 4,436
Posted By Dobri
In the attached image, the lowest smooth orange...

In the attached image, the lowest smooth orange curve is the plot of x1/2ln(ln(ln(x)))/(2*ln(x)).
The gray smooth curve above it is the plot of Kx1/2ln(ln(ln(x)))/(2*ln(x)) with an empirically...
Forum: Dobri 2022-05-14, 14:34
Replies: 53
Views: 4,436
Posted By Dobri
This update contains images of the values of the...

This update contains images of the values of the absolute minima and maxima (up to a prime x on the horizontal axis) of the prime race โˆ†(x) = ๐œ‹6,5(x) - ๐œ‹6,1(x) for the first 185,000,000,000 primes....
Forum: Dobri 2022-05-13, 05:43
Replies: 26
Views: 1,637
Posted By Dobri
Excluding the 3rd Mersenne prime number M5 (for...

Excluding the 3rd Mersenne prime number M5 (for which p = 5, p mod 4 = 1, 2p - 1 = 6p + 1 = 27ร—12 + 22 = 31 is a prime, and also 2p + 1 = 11 is a prime):

1) Out of the total of 50,847,534 prime...
Forum: Lounge 2022-05-12, 14:01
Replies: 49
Views: 2,251
Posted By Dobri
Alexander Grothendieck ...

Alexander Grothendieck
https://en.wikipedia.org/wiki/Alexander_Grothendieck
Forum: Number Theory Discussion Group 2022-05-06, 16:01
Replies: 12
Views: 762
Posted By Dobri
The Wolfram code below represents the prime...

The Wolfram code below represents the prime exponent p of each known Mersenne prime 2p-1 as a unique sum of two squares p = a2 + b2 with the exception of the prime exponents p = 4k + 3 for which...
Forum: MattcAnderson 2022-05-02, 21:54
Replies: 6
Views: 283
Posted By Dobri
Marin Mersenne wrote about the birds that ...

Marin Mersenne wrote about the birds that

"...qu'ils se seruent de leurs voix pour exprimer leurs passions naturelles, & non des paroles..."
("...they use their voices to express their...
Forum: Information & Answers 2022-05-02, 15:39
Replies: 11
Views: 1,499
Posted By Dobri
Below is a link to one external thread related to...

Below is a link to one external thread related to the discussion.
https://forums.tomshardware.com/threads/prime95-worker-failing.3457965
Forum: Lounge 2022-04-24, 17:57
Replies: 1,925
RIP
Views: 217,445
Posted By Dobri
My condolences as you grieve, xilman.

My condolences as you grieve, xilman.
Forum: Dobri 2022-04-24, 08:25
Replies: 12
Views: 1,515
Posted By Dobri
For quality assurance (QA) purposes, a stage-1...

For quality assurance (QA) purposes, a stage-1 P-1 test was performed on M726064763 without excluding in quotation marks the 12 known factors.
The result is a 145-digit 481-bit composite factor...
Forum: No Prime Left Behind 2022-04-23, 10:42
Replies: 24
Views: 645
Posted By Dobri
All three pages are accessible with Chromium for...

All three pages are accessible with Chromium for Raspberry Pi 4B.
Forum: Math 2022-04-22, 11:41
Replies: 2
Views: 850
Posted By Dobri
Here is a Wolfram code to test the quoted...

Here is a Wolfram code to test the quoted heuristic recursion. :smile:

p = 1277; Mn = 2^p - 1; xn = 3;
While[(GCD[xn - 1, Mn] == 1) && (xn != 0), xn = Mod[(xn^(12*p*5) - 1)*(xn^(12*p*7) - 1) + 1,...
Forum: Dobri 2022-04-20, 12:58
Replies: 26
Views: 1,637
Posted By Dobri
This forms a sequence of composite p values...

This forms a sequence of composite p values indeed,
p = 21, 121, 153, 221, 237, 245, 305, 333, 357, 381, 445, 465, 545, 565, 605, 637, 657, 737, 753, 777, 793, 861, 917,...


kc = 3; ic = 2;...
Forum: Dobri 2022-04-20, 10:19
Replies: 26
Views: 1,637
Posted By Dobri
It should be noted that it is assumed that 6p + 1...

It should be noted that it is assumed that 6p + 1 is a prime number.
If 6p + 1 is not a prime number, there are instances when Mp mod (6p + 1) โ‰  0 and 6p + 1 = 27a2 + b2, for example:
p = 41, (241...
Forum: Dobri 2022-04-20, 09:29
Replies: 26
Views: 1,637
Posted By Dobri
I just connect a Raspberry Pi 4B device to the...

I just connect a Raspberry Pi 4B device to the HDMI port of my 4K TV set and use Wolfram Mathematica for free.
Here is the Wolfram code for the Mersenne primes

MPData = {2, 3, 5, 7, 13, 17, 19,...
Forum: Dobri 2022-04-20, 07:58
Replies: 26
Views: 1,637
Posted By Dobri
There is a typo, it has to be "... for p = 101,...

There is a typo, it has to be "... for p = 101, 137, 173, 181, 241, 257, 277, 293, 313,..."
Forum: Dobri 2022-04-20, 06:48
Replies: 26
Views: 1,637
Posted By Dobri
Excluding p = 5 for which 25 - 1 = 6ร—5 + 1 =...

Excluding p = 5 for which 25 - 1 = 6ร—5 + 1 = 27ร—12 + 22, there are no other counterexamples for p mod 4 = 1 and k = 3 within the limited sample of known Mersenne primes.

Starting from the...
Forum: Dobri 2022-04-20, 05:14
Replies: 26
Views: 1,637
Posted By Dobri
Here is a counterexample: p = 5, p mod 4 = 1, and...

Here is a counterexample: p = 5, p mod 4 = 1, and 2p - 1 = 6p + 1 = 27ร—12 + 22 is the 3rd Mersenne prime number M5.
Forum: Dobri 2022-04-19, 16:25
Replies: 26
Views: 1,637
Posted By Dobri
Concerning k = 5, there are 10 known Mersenne...

Concerning k = 5, there are 10 known Mersenne primes, with prime exponents p = 3, 7, 13, 19, 31, 1279, 2203, 2281, 23209, and 44497, for which 2*5*p+1 is a prime number. Here p mod 6 = 1 for p = 7,...
Forum: Dobri 2022-04-19, 15:52
Replies: 26
Views: 1,637
Posted By Dobri
Within the limited sample of known Mersenne...

Within the limited sample of known Mersenne primes, there are 7 Mersenne primes, with prime exponents p = 2, 5, 89, 9689, 21701, 859433, and 43112609, for which 2p + 1 is a prime number. Obviously, p...
Forum: Dobri 2022-04-19, 15:14
Replies: 11
Views: 1,175
Posted By Dobri
Addendum: A typo (an accidental inclusion of the...

Addendum: A typo (an accidental inclusion of the k term) has been made inadvertently in the previous post #11,
https://www.mersenneforum.org/showpost.php?p=604211&postcount=11.
Therefore, post #11...
Forum: Dobri 2022-04-18, 16:17
Replies: 11
Views: 1,175
Posted By Dobri
If xp-1+xp-2+...+x+1 = (x+p)(x+...)... over the...

If xp-1+xp-2+...+x+1 = (x+p)(x+...)... over the integers modulo 2kp+1,
then 2kp+1 is a factor of the composite Mersenne number Mp.

Also, if 2kp+1 is a factor of a composite Mersenne number Mp, ...
Forum: Dobri 2022-04-18, 14:06
Replies: 26
Views: 1,637
Posted By Dobri
The information in this thread is provided for...

The information in this thread is provided for completeness and is not concerned with novelty indeed.
Searching for "1655600", two previous posts on the topic can be located, see...
Forum: Dobri 2022-04-17, 16:08
Replies: 26
Views: 1,637
Posted By Dobri
Mersenne Numbers Known from Number Theory to Be Composite

The Mersenne numbers with prime exponents p > 3 for which p mod 4 = 3 and 2p + 1 is a prime number are known to be composite.
Out of the total of 50,847,534 prime exponents 2 โ‰ค p โ‰ค 999,999,937,...
Forum: Dobri 2022-04-13, 19:30
Replies: 16
Views: 1,155
Posted By Dobri
The Wolfram function FindInstance is used merely...

The Wolfram function FindInstance is used merely as an illustration.
The intended discussion in this thread is on the framework for prospective utilization of additional empirical constraints....
Forum: Dobri 2022-04-13, 14:22
Replies: 16
Views: 1,155
Posted By Dobri
The result was obtained for approximately one...

The result was obtained for approximately one hour while running the Wolfram code in interpreter mode on a Raspberry Pi 4B device for which Wolfram Mathematica is available for free. Compiling the...
Showing results 1 to 25 of 317

 
All times are UTC. The time now is 06:17.


Thu May 19 06:17:58 UTC 2022 up 35 days, 4:19, 0 users, load averages: 1.43, 1.40, 1.34

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”