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Search: Posts Made By: Dobri
Forum: Dobri 2022-08-14, 07:59
Replies: 51
Views: 4,763
Posted By Dobri
Thanks, this flawlessly eliminates the cases for...

Thanks, this flawlessly eliminates the cases for k = 12m + 8 and 12m + 11 indeed.
Also, divisibility by 3 is observed for k = 12m + 5 since 2(12m + 5)(6n + 5) + 1 gives the coefficient 2×5×5 + 1 =...
Forum: Dobri 2022-08-13, 10:15
Replies: 51
Views: 4,763
Posted By Dobri
Thanks, this nicely eliminates the cases for k =...

Thanks, this nicely eliminates the cases for k = 12m + 1, 12m + 5, and 12m + 9 indeed.

However, the cases for k = 12m + 8 and 12m + 11 still need a theoretical interpretation.
I do not have a...
Forum: Dobri 2022-08-11, 11:10
Replies: 51
Views: 4,763
Posted By Dobri
A repetitive pattern in observed after k = 12 for...

A repetitive pattern in observed after k = 12 for the primes p and the values of k for which primes 2kp + 1 can be found that divide the Mersenne numbers 2p - 1,
see the previous posts #29 and #30...
Forum: Dobri 2022-08-07, 19:25
Replies: 19
Views: 2,395
Posted By Dobri
I am using Prime 95 version P95v30.8b15 for P-1...

I am using Prime 95 version P95v30.8b15 for P-1 tests while waiting in anticipation for a stable version of P95v30.9 to run ECM more efficiently.

That is correct, the Ghz-Days statistics for...
Forum: Dobri 2022-08-07, 17:25
Replies: 19
Views: 2,395
Posted By Dobri
My submitted P-1 tests on M1277 and M1619 were...

My submitted P-1 tests on M1277 and M1619 were performed with Intel Core i7-7700 @ 3.60GHz and just 16GB RAM. Let's assume that many users have much better computers and more RAM.
Forum: Dobri 2022-08-07, 06:51
Replies: 19
Views: 2,395
Posted By Dobri
Perhaps more P-1 tests could factor at least one...

Perhaps more P-1 tests could factor at least one of the remaining unfactored Mersenne numbers for small exponents:
M1277, M1619, M1753, M2267, M2273, M2423, M2521, M2713, M2719, M2851, M3049,...
Forum: Lounge 2022-07-28, 07:53
Replies: 13
Views: 303
Posted By Dobri
"Living 'dead' man gets long delayed new ID card"...

"Living 'dead' man gets long delayed new ID card"
https://www.bangkokpost.com/thailand/general/2354522/living-dead-man-gets-long-delayed-new-id-card
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-26, 17:42
Replies: 29
Views: 3,448
Posted By Dobri
I was able to construct the distinct words only...

I was able to construct the distinct words only after listening to the voice of a female singer from Venezuela,
see https://soundcloud.com/gustavocolina/14-tata-quillacas-folclore.
The higher...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-25, 20:21
Replies: 29
Views: 3,448
Posted By Dobri
This is more likely "Bendición-inta quwasun ...

This is more likely
"Bendición-inta quwasun

Qucha nincha qespichispa
Kuti-y ninchista saqespa".
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-24, 07:04
Replies: 29
Views: 3,448
Posted By Dobri
The following single paragraph is translated from...

The following single paragraph is translated from Spanish language and provided below for scholarly purposes:

“2. The miracle in the cult of the Lord of Quillacas
Legend has it that at some point...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-23, 21:55
Replies: 29
Views: 3,448
Posted By Dobri
Indeed, the OP provides a link to a traditional...

Indeed, the OP provides a link to a traditional version of the song performed by the Peruvian band Inkari where an "s" sound for "Quillacas" can be heard.
However, Bolivian performers tend to...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-23, 20:33
Replies: 29
Views: 3,448
Posted By Dobri
Quillaka is the name of one of the Aymara tribes....

Quillaka is the name of one of the Aymara tribes.
Perhaps the "s" in Quillacas is a Spanish suffix and the use of "c" instead of "k" is also of Spanish origin.
One could listen to a shortened...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-23, 18:13
Replies: 29
Views: 3,448
Posted By Dobri
This is more likely "Chaya-y-ta-wan...

This is more likely

"Chaya-y-ta-wan k’ancha-ku-sun
Qunqur chaki maña-ku-sun",

where "qunqur" means knee.

Note: The phrase "qunqur chaki" is found twice in the national anthem of Bolivia...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-23, 16:15
Replies: 29
Views: 3,448
Posted By Dobri
In Colombia, ñaña means a sister of a woman, thus...

In Colombia, ñaña means a sister of a woman, thus a woman can call her sister ñaña, but a man could call ñaña only a sister of his wife.
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-23, 08:14
Replies: 29
Views: 3,448
Posted By Dobri
The first four lines could be written as follows:...

The first four lines could be written as follows:


"Chaya-y-ta chaya-sun-pu-ni
Tata Quillakas-man-pu-ni
Ñañita-y qanwan kusqa
Kusi-y kawsa-y-ta kutin-pu-sun",


where "-ta" is a...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-23, 06:27
Replies: 29
Views: 3,448
Posted By Dobri
It seems that "-sun-pu-ni" and "-man-pu-ni" are...

It seems that "-sun-pu-ni" and "-man-pu-ni" are not distinct words bur rather consecutive suffixes to the preceding words.
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-18, 11:31
Replies: 29
Views: 3,448
Posted By Dobri
There is some limited inclusion of Spanish...

There is some limited inclusion of Spanish elements indeed.
For example, ñaña means sister-in-law, then the Spanish suffix -ita is added to have ñañita, and then the Quechua suffix -y is added to...
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-17, 13:49
Replies: 29
Views: 3,448
Posted By Dobri
A more precise written version is "Ñañitay...

A more precise written version is
"Ñañitay qanwan kusqa"
where "kusqa" means 'together'.


Actually, the word "kutin" without additional suffixes means 'again'.
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-15, 22:58
Replies: 29
Views: 3,448
Posted By Dobri
The last line of the last couplet seems to be ...

The last line of the last couplet seems to be

"Kusi-y kawsa-y-ta kutin-pu-sun",

where "kusi-y" means 'happiness' ('gaiety' or 'merrily'),
"kawsa-y" means 'life',
and "kutin" means 'return'....
Forum: Languages -- Ancient & Modern, Human & Machine 2022-07-07, 05:27
Replies: 29
Views: 3,448
Posted By Dobri
The third line seems to be "Ña ñi tay k'a huan...

The third line seems to be
"Ña ñi tay k'a huan cus ca"
(Mi' Mi' Sol' Mi' Re' Do' La).
Forum: Dobri 2022-06-09, 10:15
Replies: 51
Views: 4,763
Posted By Dobri
This is a continuation of the previous post #29...

This is a continuation of the previous post #29 at https://www.mersenneforum.org/showpost.php?p=606844&postcount=29.

Number of 2kp+1 primes for p within the range 2 ≤ p ≤ 999,999,937 which...
Forum: Dobri 2022-05-30, 22:54
Replies: 51
Views: 4,763
Posted By Dobri
Number of 2kp+1 primes for p within tne range 2 ≤...

Number of 2kp+1 primes for p within tne range 2 ≤ p ≤ 999,999,937 which divide the composite Mersenne numbers Mp = 2p-1 so that Mp mod (2kp+1) = 0:

k=1: 1655600 (for which p mod 4 = 3 and p mod 6...
Forum: Homework Help 2022-05-30, 22:52
Replies: 4
Views: 1,295
Posted By Dobri
See also the web page on "Euler and Lagrange on...

See also the web page on "Euler and Lagrange on Mersenne Divisors" by Chris K. Caldwell at <https://primes.utm.edu/notes/proofs/MerDiv2.html>.
Forum: Homework Help 2022-05-25, 09:17
Replies: 4
Views: 1,295
Posted By Dobri
For the first known proof, see the following...

For the first known proof, see the following manuscript:
Joseph Louis de Lagrange, Recherches d'arithmétique (1775), pp. 695-795 (in French).
Available:...
Forum: Homework Help 2022-05-24, 23:11
Replies: 4
Views: 1,295
Posted By Dobri
See the following manuscript: Édouard Lucas,...

See the following manuscript:
Édouard Lucas, Théorie des Fonctions Numériques Simplement Périodiques, American Journal of Mathematics, Vol. 1, No. 4 (1878), pp. 184-240 and 289-321 (in French). ...
Showing results 1 to 25 of 343

 
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