New Mersenne Conjecture
 

The New Mersenne (Prime) Conjecture is basically saying if a prime p is an exponent for both a Mersenne Prime (2[sup]p[/sup]-1) and a Wagstaff prime (2[sup]p[/sup]+1)/3 then p is of the form 2[sup]k[/sup] +/- 1 or 4[sup]k[/sup] +/- 3 where k is some natural number. The conjecture says that if 2 of these conditions is true then so is the third.

I tried submitting some updates a few times to the list here:
[url]http://primes.utm.edu/mersenne/NewMersenneConjecture.html[/url]
but it seems it is not being updated anymore.

So I made a new list myself: [B][URL="http://www.hoegge.dk/mersenne/NMC.html"]NMC.html[/URL][/B]

The conjecture corresponds to there being only 1 or 3 "yes" in each horizontal line. If 2 yes occurred the conjecture would be false.
The green lines are where the conjecture holds, and the 2 red lines are still unknown.




Here are the updates I made since the old list:
p=11213, p=216091, p=1398269: Added factors of (2[sup]p[/sup]+1)/3 found on factordb.com

p=65537: Added factor of 2[sup]p[/sup]-1 found on mersenne.org

p=986191, p=4031399, p=13347311, p=13372531: Added the 4 lines for the new Wagstaff primes with factors of 2[sup]p[/sup]-1 from mersenne.org

p=20966011, p=30402457, p=32582657, p=37156667, p=42643801, p=43112609, p=57885161:
Added the 7 latest Mersenne Primes. Found factors of 3 of the Wagstaff numbers with LLR, and factored the rest to 69-70 bits. Ran the Vrba-Reix test with LLR on the remaining 4 Wagstaff numbers proving them composite:
(2^20996011+1)/3 is not prime. Vrba-Reix RES64: BA75673D7BAB002F Time : 566688.538 sec.
(2^30402457+1)/3 is not prime. Vrba-Reix RES64: 9AD14D52DFCCB2A6 Time : 887355.947 sec.
(2^32582657+1)/3 is not prime. Vrba-Reix RES64: 99985D4C1756CE0F Time : 946154.777 sec.
(2^42643801+1)/3 is not prime. Vrba-Reix RES64: 90ACCFA9ADA98C0D Time : 1575885.158 sec.

p=268435459, p=1073741827: Added these 2 lines so the list roughly goes to p=1 billion like primenet v5. Found 1 factor of Wagstaff number with LLR and factored the other to 76 bits without success. Factored the 2 Mersenne numbers to 80 and 82 bits with mfaktc without success.

Is the conjecture merely motivated by observation that it works for small p and the probability that two of the conditions (let alone three) are satisfied very quickly becomes vanishingly small? (And hence the conjecture is expected to hold in rather the same way that the conjecture of no Fermat primes beyond F[sub]4[/sub] is expected.)

Or is it in fact conjectured that there are more occurrences of all three conditions holding beyond the last known case of p=127?

[QUOTE=Brian-E;369981]Is the conjecture merely motivated by observation that it works for small p and the probability that two of the conditions (let alone three) are satisfied very quickly becomes vanishingly small?
[/QUOTE]

Yes. Furthermore, John indicated that he was not really serious
when he proposed it.

This "conjecture" is basically a joke.

I always thought that NMC was [B]inspired[/B] by Mersenne's original conjecture list 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, which indeed picks out primes of the form 2^k+/-1 and 4^k+/-3 (except 61, which, while of the form 4^k-3 and in fact gives a Mersenne prime, was left out by Mersenne). Could be a coincidence though.

[QUOTE=axn;369991]I always thought that NMC was [B]inspired[/B] by Mersenne's original conjecture list 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, which indeed picks out primes of the form 2^k+/-1 and 4^k+/-3 (except 61, which, while of the form 4^k-3 and in fact gives a Mersenne prime, was left out by Mersenne). Could be a coincidence though.[/QUOTE]

One good joke deserves another.

[QUOTE=ewmayer;370014]One good joke deserves another.[/QUOTE]

Can we test the validity of it in this thread ? There's a pattern in the difference between (2^(2n+1) + 1)/3 and the next Mersenne number. Basically, A080674 with an extra 0 on the front. Could we test the validity of it based on this ? Admittedly, I have a portfolio to complete for school, so I might get around to it myself.

[QUOTE=R.D. Silverman;369985]This "conjecture" is basically a joke.[/QUOTE]

Yes. It seems to be an example of a theorem which is true by coincidence. (I would love to be proved wrong here!)

Hello ewmeyer I do not get here often, but I recall a reason to respect you
 

[QUOTE=ewmayer;370014]One good joke deserves another.[/QUOTE]
Some think, weight givens, speak without reaching conclusion missing some step. Given; more can be known than is capable of being penetrated by mere mortal logic at some moment. I may have read Mersenne's list may be uncertain in regards to 61 or 67 ie, reading his hand writing. If you please to confirm the following... your friends may be pleased to wager conjectures entrusting all to TIME ; as she alone has proven herself a noble guardian of all entrusted unto her, whether mortal or divine. On the quantity of members of ( S ) less than a given term of G. Let K be a known prime such that 2^K-1 is prime D, such that D(D+1)/2 is some S, sum of her parts. Let G0= triangular radix of 8 = 3.5311... Zero S less than G0. G1=8, G2=36, G3=666, all terms of G follow by triangulation of 8. The members of S show an increase. Present knowledge of proper order of S being incomplete though perhaps correct up to G28. At G30 we delight in desire to know. K.D.S projects merely 53 as a divine statement. All such being feminine intuitive conjectures divined in TIME. When will 5 be proven in any term? Then 6,7,8...should mortals divine no logic in such trivial beauties?

[QUOTE=Kathegetes;370054]Some think, weight givens, speak without reaching conclusion missing some step. Given; more can be known than is capable of being penetrated by mere mortal logic at some moment. I may have read Mersenne's list may be uncertain in regards to 61 or 67 ie, reading his hand writing. If you please to confirm the following... your friends may be pleased to wager conjectures entrusting all to TIME ; as she alone has proven herself a noble guardian of all entrusted unto her, whether mortal or divine. On the quantity of members of ( S ) less than a given term of G. Let K be a known prime such that 2^K-1 is prime D, such that D(D+1)/2 is some S, sum of her parts. Let G0= triangular radix of 8 = 3.5311... Zero S less than G0. G1=8, G2=36, G3=666, all terms of G follow by triangulation of 8. The members of S show an increase. Present knowledge of proper order of S being incomplete though perhaps correct up to G28. At G30 we delight in desire to know. K.D.S projects merely 53 as a divine statement. All such being feminine intuitive conjectures divined in TIME. When will 5 be proven in any term? Then 6,7,8...should mortals divine no logic in such trivial beauties?[/QUOTE]


What kind of drugs are you taking?

[QUOTE=R.D. Silverman;370060]What kind of drugs are you taking?[/QUOTE]

Or perhaps (of the psychotropic variety) *not* taking? :confused:

[QUOTE=NBtarheel_33;370065]Or perhaps (of the psychotropic variety) *not* taking? :confused:[/QUOTE]

I must be not taking the same drugs. I couldn't even follow it.

Perhaps a Google Translate from otherwise readable French?

Or an April Fool posted from a time zone where it was already 1 April. Don't assume the location is necessarily correct.

The quote from ewmayer strongly suggests it's a joke.

Chris

[QUOTE=chris2be8;370163]Or an April Fool posted from a time zone where it was already 1 April. Don't assume the location is necessarily correct.

The quote from ewmayer strongly suggests it's a joke.

Chris[/QUOTE]

Perhaps. However, based upon prior posts from the same poster, I am
not sure. It is on the same intellectual level as some of the OP's prior
posts.

[QUOTE]This "conjecture" is basically a joke.[/QUOTE]I humbly suggest a new mathematical term: [B]conjoketure[/B],

- - - -

Folks,

[U]This may be original! You read it here first![/U]

Neither a Google search nor a Yahoo! search on "conjoketure" returns any result.

[quote=Google]Did you mean:
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[URL="https://www.google.com/search?q=conjointure&spell=1&sa=X&ei=Qv09U-5Nss2xBNq-goAH&ved=0CCYQBSgB"][B][I]conjointure[/I][/B][/URL]

[URL="https://www.google.com/search?q=conjugateur&spell=1&sa=X&ei=Qv09U-5Nss2xBNq-goAH&ved=0CCcQBSgC"][B][I]conjugateur[/I][/B][/URL]

[URL="https://www.google.com/search?q=conjoncture&spell=1&sa=X&ei=Qv09U-5Nss2xBNq-goAH&ved=0CCgQBSgD"][B][I]conjoncture[/I][/B][/URL]




No results containing all your search terms were found.
Your search - [I]conjoketure[/I] - did not match any documents.
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[/quote]

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[B]Did you mean [URL="http://search.yahoo.com/search;_ylt=A0LEV0ya_D1TDA8A.CZXNyoA?ei=UTF-8&norw=1&fr=moz35&p=%2Bconjecture"]+ [B][I]conjecture[/I][/B][/URL][/B]

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OTOH, it's hard to believe that "conjoketure" has never before been pronounced in some hall of academe.

[QUOTE=cheesehead;370273]OTOH, it's hard to believe that "conjoketure" has never before been pronounced in some hall of academe.[/QUOTE]
You'd expect so if the same sort of joke has been worked out before by serious mathematicians. Is there anything else comparable?

I wonder who chose the name "New Mersenne Conjecture". That strikes me as possibly tongue-in-cheek in itself, sounding rather grand and at the same time possibly digging at the large number of arbitrary, unproven and probably unprovable statements which people have already made before in Number Theory.

Perhaps I'll get a citation in a future edition of the OED because I first put it in publicly-accessible written form.

[QUOTE=cheesehead;370273]I humbly suggest a new mathematical term: [B]conjoketure[/B][/QUOTE]Cool.[QUOTE=cheesehead;370741]Perhaps I'll get a citation in a future edition of the OED because I first put it in publicly-accessible written form.[/QUOTE]Oops, not so humble anymore. :showoff:

:razz:

Humble fame.

[QUOTE=R.D. Silverman;369985]Yes. Furthermore, John indicated that he was not really serious
when he proposed it.

This "conjecture" is basically a joke.[/QUOTE]

Nowadays math is full with conjectures! Missing the proofs!
Euclid would rotate in his grave when he knew what math turned into the last 2000 years.

[QUOTE=ATH;369976]So I made a new list myself: [B][URL="http://www.hoegge.dk/mersenne/NMC.html"]NMC.html[/URL][/B]
[/QUOTE]

You can extended the table to include more terms in [URL="https://oeis.org/A122834"]A122834[/URL], now this table includes all known Mersenne exponents ([URL="https://oeis.org/A000043"]A000043[/URL]) and all known Wagstaff exponents ([URL="https://oeis.org/A000978"]A000978[/URL]), but only include [URL="https://oeis.org/A122834"]A122834[/URL](n) for n<=27, currently both WM61 and WM127 have known prime factors (1328165573307087715777 and 886407410000361345663448535540258622490179142922169401, respectively), although neither [URL="http://www.doublemersennes.org/mm61.php"]MM61[/URL] nor [URL="http://www.doublemersennes.org/mm127.php"]MM127[/URL] have known prime factor, however, if either MM61 or MM127 is prime, then the New Mersenne Conjecture would be false, you can extended the table to include all numbers in [URL="https://oeis.org/A122834"]A122834[/URL] up to M127

I suggest:

* Test all Wagstaff numbers with exponent below 15 million (at least prove or disprove that 13347311 and 13372531 are the next two Wagstaff exponents after 4031399), W13347311 and W13372531 are discovered in 2013 (8 years ago!!!), but currently [URL="https://mersenneforum.org/showthread.php?t=24185"]only the Wagstaff numbers with exponent below 10 million are tested[/URL].
* Prove the primality of W95369, [URL="http://factordb.com/index.php?id=1100000000017713329"]W83339[/URL] has been proven prime in 2014 (7 years ago!!!), and W95369 is just a little larger than it, also recently a much larger number [URL="https://www.ellipsa.eu/public/primo/top20.html"]Partition(1289844341)[/URL] has been proven prime with Primo.
* Test the Mersenne numbers and the Wagstaff numbers with exponent [URL="https://oeis.org/A122834"]A122834[/URL](n) for 29<=n<=34 (for n=28 and n=35, the corresponding Mersenne numbers are double Mersenne numbers MM61 and MM127, and both have no known prime factors, and the corresponding Wagstaff numbers are both factored and hence proven to be composite) (all these numbers are too large to use primality tests such as [URL="https://primes.utm.edu/prove/prove3_1.html"]N-1 primality test[/URL], [URL="https://primes.utm.edu/prove/prove3_2.html"]N+1 primality test[/URL], [URL="https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test"]Miller-Rabin primality test[/URL], [URL="https://mathworld.wolfram.com/Baillie-PSWPrimalityTest.html"]Ballie-PSW primality test[/URL], we can only use [URL="https://primes.utm.edu/glossary/page.php?sort=TrialDivision"]trial division[/URL] to find a divisor of the numbers to disprove their primality)

[QUOTE=sweety439;581702]I suggest:[/QUOTE]

You seem to have a lot of suggestions for what others should do with their time and CPU resources. Are you planning on contributing any of yours?

:goodposting:

This 1 april joke posting from 7 years ago is still alive?

[QUOTE=diep;582320]This 1 april joke posting from 7 years ago is still alive?[/QUOTE]

Premium Aprils last longer.

W82589933 has the factor 17973642059656480077259129
WM127 has the factor 886407410000361345663448535540258622490179142922169401

Those were discovered in 2020.
[url]http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html[/url]

[url]http://www.hoegge.dk/mersenne/NMC.html[/url] should be updated.