Gaussian-Mersenne & Eisenstein-Mersenne primes - Page 2

Andrew Usher · 2022-12-16, 14:09

That is the page for Gaussian Mersennes. I was suggesting that Eisenstein Mersennes likewise be identified, though I wouldn't insist they have their own page - this is what my comment was about in the first place.

The two are practically isomorphic classes - and the only two such classes.

Batalov · 2023-06-18, 21:37

Eisenstein Mersenne Norm prime #27 (?) is found: Phi(6,3^1444194-1)/3 (corrected; thx, J!)
This prime may also be written as: 3^2888387-3^1444194+1

Btw, towards the earlier questions, some more (easily found) links:
- OEIS: A066408
- I remember that I salvaged from the now-perished Yahoo groups (Primeform group), Mike Oakes' message that is a very good read. It would have been even harder to find now, 10 years later.
- There are messages from Mike Oakes on NMBRTHRY archives, too.
- The method of direct primality proof is implemented from Theorem 3.4 (2) from Berrizbeitia, Iskra, 2010 paper.

JeppeSN · 2023-06-18, 23:57

Quote:

Originally Posted by Batalov

Eisenstein Mersenne Norm prime #27 (?) is found: Phi(3,3^1444194-1)/3
This prime may also be written as: 3^2888387-3^1444194+1

Should it not have been Phi(3, -3^1444194+1)/3 instead? /JeppeSN

Batalov · 2023-06-19, 00:09

Ah, true.

I will resubmit. Nobody edits the "key value" in the database (even Chris didn't like to; he requested re-submits).

These are so far between, that the last one was submitted by Iskra. ... in 2005!

Phi(6,3^1444194-1)/3 = Phi(3,-3^1444194+1)/3

Batalov · 2023-06-30, 18:04

Followed with EM₂₈ = 3^4043119+3^2021560+1 (1929059 digits)

and EM₂₉ = 3^6608603-3^3304302+1 (3153105 digits)

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Distribution of Mersenne primes before and after couples of primes found	emily	Math	35	2022-12-21 16:32
Mersenne Primes p which are in a set of twin primes is finite?	carpetpool	Miscellaneous Math	4	2022-07-14 02:29
Search for prime Gaussian-Mersenne norms (and G-M-cofactors)	Cruelty	Proth Prime Search	158	2020-07-31 22:23
What's the use for Mersenne primes?	preda	Lounge	24	2018-01-16 01:40
Mersenne Wiki: Improving the mersenne primes web site by FOSS methods	optim	PrimeNet	13	2004-07-09 13:51

2022-12-16, 14:09	#12
Andrew Usher Dec 2022 773₈ Posts	That is the page for Gaussian Mersennes. I was suggesting that Eisenstein Mersennes likewise be identified, though I wouldn't insist they have their own page - this is what my comment was about in the first place. The two are practically isomorphic classes - and the only two such classes.

2023-06-18, 21:37	#13
Batalov "Serge" Mar 2008 San Diego, Calif. 3²×7×163 Posts	Eisenstein Mersenne Norm prime #27 (?) is found: Phi(6,3^1444194-1)/3 (corrected; thx, J!) This prime may also be written as: 3^2888387-3^1444194+1 Btw, towards the earlier questions, some more (easily found) links: - OEIS: A066408 - I remember that I salvaged from the now-perished Yahoo groups (Primeform group), Mike Oakes' message that is a very good read. It would have been even harder to find now, 10 years later. - There are messages from Mike Oakes on NMBRTHRY archives, too. - The method of direct primality proof is implemented from Theorem 3.4 (2) from Berrizbeitia, Iskra, 2010 paper.

2023-06-19, 00:09	#15
Batalov "Serge" Mar 2008 San Diego, Calif. 3²×7×163 Posts	Ah, true. I will resubmit. Nobody edits the "key value" in the database (even Chris didn't like to; he requested re-submits). These are so far between, that the last one was submitted by Iskra. ... in 2005! Phi(6,3^1444194-1)/3 = Phi(3,-3^1444194+1)/3

2023-06-30, 18:04	#16
Batalov "Serge" Mar 2008 San Diego, Calif. 3²·7·163 Posts	Followed with EM₂₈ = 3^4043119+3^2021560+1 (1929059 digits) and EM₂₉ = 3^6608603-3^3304302+1 (3153105 digits)