Other Primes
 

I thought it would be nice to have a thread discussing primes found by others, or by us but not related to RPS.

And the first one is
2^1203793-2^601897+1 (362378 digits)

new [URL="http://primes.utm.edu/top20/page.php?id=41"]Gaussian Mersenne norm[/URL] record set by Cruelty. More details can be found [URL="http://www.mersenneforum.org/showthread.php?p=87695#post87621"]here[/URL]

Congratulations!

The form can be searched using the latest version of LLR (3.7.x). I tried once at 400k but it was a bit time consuming (on my laptop) and I gave up.

Earlier this month I found 99*10^139670-1, the new [URL="http://primes.utm.edu/top20/page.php?id=15"]Near-repdigit[/URL] record. In fact, 10 of the top 20 for this form have been entered in the last
2-3 months.

Badges marking the latest 9.8M-digit Mersenne prime are available in [URL="http://www.mersenneforum.org/showthread.php?t=6421"]this thread[/URL]. Sign up there if you'd like to have one.

(2^1127239+2^563620+1)/5 is 3-PRP!, which AFAIK is the largest GQ so far :smile:
The question I have now is, how to prove it is, or it is not a prime :question:
BTW: I don't consider using PRIMO or other ECPP based software for this purpose as it would take more than my life to complete :rolleyes:

Replies to the above post moved to a separate thread:

[URL="http://www.mersenneforum.org/showthread.php?t=6657"]GQ(1127239) is PRP![/URL]

Please post further replies there.

Check [URL="http://primes.utm.edu/primes/page.php?id=78939"]this[/URL] out :shock:

Yes, huge
26773*2^2465343-1, 742147 digits.

20th of all times!
Note that now an entry to Top-100 requires binary exponent n>1.2M !

Monster
 

Someone, outside of this group I think has posted a monster

[url]http://primes.utm.edu/primes/page.php?id=79192[/url]

21st largest prime every found!!!

That's L191, S. Banka who is (unfortunately :smile: ) not with us. He found 5 large primes in only one year, he began with 12121 project but now he is testing k=737 (=11*67) alone. He is now 13th by score!:surprised 4 of his 5 primes are currently in top-100, only Cooper and Heuer have more primes in top-100 while Grobstich has 4 too.

[QUOTE=Kosmaj;96369]... while Grobstich has 4 too.[/QUOTE]

... and Thomas has 4 in the Top-101. :grin:

Congrats to David Underbakke (L99) who just reported new largest Sophie-Germain pair (51910 digits):
48047305725*2^172403-1
48047305725*2^172404-1

Only 10 days after the new twin record!

New record Woodall :surprised What a surprise! :shock:

[URL="http://primes.utm.edu/primes/page.php?id=79267"]1268979*2^1268979-1 [/URL] (382007 digits)

Discovered by W. Siemelink using LLR (L201). Congrats!

Check [URL="http://primes.utm.edu/primes/page.php?id=79378"]this[/URL] out. [B]k>60bit[/B] found using [B]LLR[/B]

I hope my post won't clutter up this thread too much ; my excuses in advance if so, and moderators, please move it to wherever it should be if this place is not OK !
I just discovered the existence of LLR.
Is the search for GM's somewhere somehow coordinated ?
(People declaring to search some ranges...)
To what extend are the gmfcandidates prefactored or elsehow selected ?
I just ran llr somehow randomly on such a candidate and it IMMEDIATELY (time << 1 second) found a factor (2^16666417-...+1 has factor 18068995989053)
- how comes that this easy finding is not mentioned in the gmfcand... file while other bigger factors are there ?
Again sorry for my ignorance and maybe inappropriate posting...
PS: the llr program does not seem to write a save file when it's killed, like mprime...?

gmfcandidates is prefactored to 32 bits for both GM and GQ, meaning that only if a factor is found for both such an exponent has been eliminated... however by default LLR will look only for GMs so only GM factors will be reported. Check out LLR documentation for details.

BTW: when exiting LLR it will always save it's current progress.

[URL="http://primes.utm.edu/primes/page.php?id=80955"]New Woodall record [/URL] :tu:

[QUOTE=Cruelty;107914][URL="http://primes.utm.edu/primes/page.php?id=80955"]New Woodall record [/URL] :tu:[/QUOTE]

I am very happy. I've found now two Woodall primes in 10 months. Allthough the first two months I was unaware that they are called Woodall primes and that I wasn't the first to think of their special form n*2^n-1.

Willem.

Congratulations!!!

Jeff (L399) of TPS dumped alone about 60 primes at n=333,333 yestreday :shock: One more such dump and he will be in top-10 by number! :w00t:

Congrats to Maks and his son on new largest repunit PRP:

(10^270343-1)/9

3 Generalized Fermat primes have been reported under an anonymous account [URL="http://primes.utm.edu/primes/page.php?id=81870"]first[/URL], [URL="http://primes.utm.edu/primes/page.php?id=81869"]second[/URL], [URL="http://primes.utm.edu/primes/page.php?id=81868"]third[/URL] - congrats!

Those 3 are a pretty fortunate grouping! I'd ask "what are the chances?", but knowing this forum, someone would actually calculate it. :rolleyes:

Anyone know if primality testing generalized fermats is faster or slower than LLR for same-size riesel numbers?

-Curtis

It is really a pretty grouping, but GFs are very heavy weight, therefore I don't think it's unusual.

As for the speed, Proth.exe was specifically optimized for GF's. Maybe LLR is faster only for small k's. But Proth.exe has a limit on base [I]b[/I] (in b^2^k+1), for k=16 I think it's about 2M (so only b<2M can be tested).

As for the status of GF search, I think all values have been already extensively sieved and all them have been reserved but some people never completed their reserved ranges. Furthermore, about 2 years ago Yves Gallot who crated Proth.exe disappeared from the prime searching community, and since about that time GF projects began to lose popularity.

BTW, the account is not anonymous, it's written in the disclaimer that they were found by Dirk Schlueter who doesn't have an account on Top-5000. Most likely prof Caldwell found out about them through his private channels.

I just realized that Dirk's bases are at the 17M level, which means he didn't use Proth.exe, but most likely genefer80, another software written by Yves Gallot which can work with a base of any size. But it's much slower than Proth.exe because it is simulating 80-bit floating point precision in software. New 64-bit cpu's support 80-bit fp arithmetic nativelly but as I said Yves is not around to do the changes.

new biggest Woodall prime
 

251749*2^2013995-1 is the new No.1 Woodall Prime (606279 digits)!

[URL="http://primes.utm.edu/primes/page.php?id=81935"]Looks like "15k" is back[/URL].

With a k without a 3 or a 5 in it :grin:

From his website:
"Currently we are focusing on fixed n candidates, which are faster than fixed k searches"

Looks like [URL="http://primes.utm.edu/primes/page.php?id=82110"]another record Woodall[/URL] prime for Primegrid :tu:

Yes, amazing, the previous one also at the 2M level was found less than a month ago...

SOB striked again, with a huge prime

33661*2^7031232+1

with more than 2.1 M digits :shock: The 10th largest of all times. It's a result of their double-checking effort and thus smaller than their previous prime (at n=13M).

[quote=Kosmaj;117507]SOB striked again, with a huge prime

33661*2^7031232+1

with more than 2.1 M digits :shock: The 10th largest of all times. It's a result of their double-checking effort and thus smaller than their previous prime (at n=13M).[/quote]


Way to go seventeen-or-bust!! That makes a good case for double-checking I'd say! :smile:

3 Large GRUs
 

Congrats to Andy Steward on 3 new generalized rep-units in top-10! The largest one:
(13096^5953-1)/13095, 24506 digits

is currently second largest, about 1500 digits more than the GRU found by Larry and me 2 years ago (the world record at the time), which is now 3rd.

For each of his proven GRUs Andy provides a detailed commentary, so that with little self-study everybody can try to enter the field and find his first GRU. The commentary for the above prime can be found [URL="http://www.primes.viner-steward.org/andy/E/33281741.html"]here[/URL].

However, beware that entering Top-20 is not easy!

Kosmaj

Posts about k*10^n-1 moved to [URL="http://www.mersenneforum.org/showthread.php?t=9578"]another thread[/URL].

Please post new messages on this topic there.

New Conjectures 'R Us prime search effort
 

Hi all...

Come check out the new "Conjectures 'R Us" prime search effort [URL="http://www.mersenneforum.org/showthread.php?t=9738"]here[/URL]. There's plenty of bases and k's for everyone to search and have fun.


Gary

Check [URL="http://primes.utm.edu/primes/page.php?id=83407"]this[/URL] out... if this is part of primegrid, then we will fall to #5 I guess... (in terms of score)

[quote=Cruelty;121569]Check [URL="http://primes.utm.edu/primes/page.php?id=83407"]this[/URL] out... if this is part of primegrid, then we will fall to #5 I guess... (in terms of score)[/quote]
I don't see PrimeGrid in the prover code...though I can't imagine why someone would be searching for Woodall primes outside of PrimeGrid (since they would be duplicating a lot of work, especially the sieving work). It's roughly in the range that PrimeGrid is searching, though, so I wouldn't be surprised if it was a PrimeGrid thing, just that the finder forgot to include PrimeGrid in his prover code. (I'm sure if that's the case, though, the Prime Pages people will fix it.)

Cruelty

We can sustain this one, still 4th, but not the next larger one.

[QUOTE=Kosmaj;121588]We can sustain this one, still 4th, but not the next larger one.[/QUOTE]That is why we are all waiting for your k=7 prime :tu: + some other megabit primes are long overdue from me :wink:

Congrats to Richard (L185) on a huge prime
3139*2^3321905-1

only 3 digits shy of one million digits! He found the 9th SoB prime in 2005 (4847*2^3321063+1, 999744 digits) and is currently ranked 14th person by score.

.
 

Prof. Cooper found another very large prime:
7 * 2^3015762+1 (907836 digits).

By the way, can I somewhere find an overview how fast the different forms of numbers can be tested at the moment (for a example a comparison of the forms k*2^n-1, k*2^n+1, k*b^n+/-1)?

Yes, that's his largest prime after two Mersennes.
We are now waiting to see is it a Fermat or a GF divisor, I'm sure he is now working on those tests.

As for the processing speed, when b=2, both -1 and +1 are about the same for the given k. When b>2 it's much slower (except, of course when b is a power of 2).

4*3^311835-1 (148784 digits)
Attached is a list of primes for k=4 b=3.

[B]Cruelty[/B]

Congrats on a nice effort and a nice prime!

I remember that prof. Iskra had a special speed-up for
a^2*3^n+1, (n odd)

and found a number of large primes. I just found that [URL="http://www.ams.org/proc/2002-130-02/S0002-9939-01-06100-7/home.html"]his article[/URL] is now available free of charge! The Corollary 2.3 won't be difficult to implement uisng GMP...

Thanks :smile:
I am testing both k=2 and k=4 using PRP v.24.14 currently @ n=315000.

[URL="http://primes.utm.edu/primes/page.php?id=84401"]Another megaprime this year[/URL].

Yes, it's

24518^262144+1 (1150678 digits)

The new largest Generalized Fermat prime, found by Stephen Scott.
Currently ranked 13th.

Congrats!

[URL="http://primes.utm.edu/primes/page.php?id=84603"]Looks like we won't defend our current position in terms of score[/URL] :shock:

It's huge, congrats to them!

But it's reported jointly by two projects and they will share
credit, so we won't be far behind.

BTW, I also wonder what kind of "project" PrimeGrid is? They have reported so far twin candidates, Woodalls, and now Prime Sierpinski. They are also working on 3*2^n-1, and I heard they would like to run Proth and some generalized Woodalls. Looks to me like a team, not any particular project...

[quote=Kosmaj;131046]It's huge, congrats to them!

But it's reported jointly by two projects and they will share
credit, so we won't be far behind.

BTW, I also wonder what kind of "project" PrimeGrid is? They have reported so far twin candidates, Woodalls, and now Prime Sierpinski. They are also working on 3*2^n-1, and I heard they would like to run Proth and some generalized Woodalls. Looks to me like a team, not any particular project...[/quote]
They have lots of different "subprojects", many of which are actually just BOINC faces on existing mersenneforum prime-search projects. Each user can choose in his preferences what mix of subprojects he'd like to be assigned work from. :smile:

I meant "project" on Top-5000 rankings. Each project there is supposed to be about a particular subset of all prime types, not primes of all types.

[quote=Kosmaj;131051]I meant "project" on Top-5000 rankings. Each project there is supposed to be about a particular subset of all prime types, not primes of all types.[/quote]
Oh, I see.

Here goes another [URL="http://primes.utm.edu/bios/code.php?code=L606"]megaprime[/URL] Congratulations!

Congrats to RieselSieve on their latest prime
113983*2^3201175-1

with almost a million digits!

They are now 4th by score and we are 5th.
[CODE]
3 PrimeGrid 12.5 48.1833
4 Riesel Sieve Project 30 48.1155
5 Riesel Prime Search 616 47.9569
[/CODE]

Another k=4, b=3 prime
 

4*3^350767-1 (167359 digits)

[quote=Cruelty;134167]4*3^350767-1 (167359 digits)[/quote]

You stall the server for 13.86 hours!!! lol
Congratulations.

Verification took me 32200 seconds on a 3GHz Core2 :smile:

Another k=4, b=3 prime
 

4*3^353635-1 (168728 digits)

Congrats on yet another one, very close to the one you reported a week ago.
:shock::smile:

Thanks! It's time for k=2 prime :wink:

Benson prime:

[url=http://primes.utm.edu/primes/page.php?id=85095]19*2^1684813-1[/url]

[URL="http://primes.utm.edu/primes/page.php?id=85126"]Another one from Curtis Cooper[/URL] :tu:

Twin Prime
 

108615*2^110342+-1 is twin prime!

Comes in at 7th place :smile:

Congrats on a nice twin!

If it's not a secret how many n's did you check? I suppose you used the approach recently suggested by Robert Smith (?) Or, how many LLR tests in total?

Thanks.

[quote=Kosmaj;135790]Congrats on a nice twin!

If it's not a secret how many n's did you check? I suppose you used the approach recently suggested by Robert Smith (?) Or, how many LLR tests in total?

Thanks.[/quote]
Thanks Kosmaj.
Well, I'm not sure how much to give away because I intend to search higher and I don't know how much was pure luck and how much was technique.
I suspect a large amount of luck because it was found after just 220,000 candidates and 164 Riesel primes. (Just 10 days on all 4 cores at 3.18GHz, including sieving.)
It's a refinement of this idea:
[URL]http://mersenneforum.org/showpost.php?p=117068&postcount=6[/URL]

I'm now searching for the No.1 twin until I find one or get bored. Probably the latter.

Chris

A new k=27 prime by 12121:
27*2^1253870-1 (377454 digits)

Congrats to Frank (L65)!

This is a bit old, but Rieselsieve found a million+ digit prime a month ago:

[url]http://primes.utm.edu/primes/page.php?id=85221[/url]

Unfortunately, their website, [url]http://www.rieselsieve.com/[/url] , appears to have been down for the past two weeks.

[QUOTE=MooooMoo;138119]This is a bit old, but Rieselsieve found a million+ digit prime a month ago:

[url]http://primes.utm.edu/primes/page.php?id=85221[/url]

Unfortunately, their website, [url]http://www.rieselsieve.com/[/url] , appears to have been down for the past two weeks.[/QUOTE]

yes, i noticed this prime first in the Top-5000 database.

see [url]http://www.rieselprime.org/RieselProblem.htm[/url] too

[URL="http://primes.utm.edu/primes/page.php?id=85350"]WOW![/URL] :tu:

According to PrimeGrid news they have found a new "321" prime. This will most likely put RPS on the 7-th place in terms of score...

[quote=Cruelty;139473]According to PrimeGrid news they have found a new "321" prime. This will most likely put RPS on the 7-th place in terms of score...[/quote]


At this point, I thought that Primegrid would get full credit for the prime. I think the 321search project stopped at n=5M. (Anyone know for sure?)

You are correct, RPS lead over 321search is 4993-2608 or a 2385 difference. Assuming half-credit, it would take a prime with a score of 4770 for 321search to overtake RPS, which an exponent of n=~5.4M should be.

But I'm sure it wouldn't take long for RPS to hop back into 6th again. :smile:

[quote=gd_barnes;139542]At this point, I thought that Primegrid would get full credit for the prime. I think the 321search project stopped at n=5M. (Anyone know for sure?)

You are correct, RPS lead over 321search is 4993-2608 or a 2385 difference. Assuming half-credit, it would take a prime with a score of 4770 for 321search to overtake RPS, which an exponent of n=~5.4M should be.

But I'm sure it wouldn't take long for RPS to hop back into 6th again. :smile:[/quote]
I hear PrimeGrid has now held off on 3*2^n-1 for the time being--now they're doing 3*2^n+1 until it's caught up with the former. So, that's probably what they found, in which case they would get full credit, because 3*2^n+1 is a project they're doing all on their own.

[QUOTE=Anonymous;139551]I hear PrimeGrid has now held off on 3*2^n-1 for the time being--now they're doing 3*2^n+1 until it's caught up with the former. So, that's probably what they found, in which case they would get full credit, because 3*2^n+1 is a project they're doing all on their own.[/QUOTE]

[url]http://primes.utm.edu/primes/page.php?id=85438[/url]

another one from Benson: 9*2^2060941-1 [url]http://primes.utm.edu/primes/page.php?id=85462[/url]

First primes with more than 10M digits
 

Two new, huge Mersenne primes!

2^43112609-1, 12978189 digits, found on August 23
2^37156667-1, 11185272 digits, found on September 6

New Gen Woodall Record
 

Congrats to Hugo (p237) on the new GW record!

[URL="http://primes.utm.edu/primes/page.php?id=85721"]189620*19^189620-1[/URL] (242483 digits).

[URL="http://primes.utm.edu/primes/page.php?id=85758"]The first non-Mersenne megaprime from Curtis Cooper[/URL] :tu:

Yes, the 21st prime with more than 1 million digits, and potentially the new largest Fermat (or Gen. Fermat) divisor because of a smal K:

7*2^3511774+1 (1057151 digits)

I wonder why did he use an "x" prover's code, meaning a new search algorithm?

I sse its now been corrected and changed to OpenPFGW.

[url=http://primes.utm.edu/primes/page.php?id=85789]5*2^2460482-1[/url]

My friend Benson strikes again.

5*2^3059698-1
[URL]http://primes.utm.edu/primes/page.php?id=85814[/URL]

Another k=4, b=3 prime
 

4*3^416337-1 (198644 digits) :smile:

Another big [URL="http://primes.utm.edu/primes/page.php?id=85944"]prime[/URL] :tu:

[QUOTE=Cruelty;153404]Another big [URL="http://primes.utm.edu/primes/page.php?id=85944"]prime[/URL] :tu:[/QUOTE]

see the Constant-n Search page here [url]http://www.rieselprime.de/Data/Constant_n.htm[/url]

[URL="http://primes.utm.edu/primes/page.php?id=85969"]1003*2^2076535-1[/URL]

My friend Benson strikes again.

5*2^3569154-1
[U][url]http://primes.utm.edu/primes/page.php?id=86152[/url][/U]

he has had a lot of luck lately

4*3^423253-1 (201944 digits) :smile:

Looks like the 12121 search may have found a 1 million digit prime [url]http://primes.utm.edu/primes/page.php?id=86608[/url]

The verification failed :sad:

The question now is whether it was a typo, or a software or hardware error.

Anyway, I wish them to find their first mega-digit prime soon!

Cullen record
 

Congrats to PrimeGrid on the new record Cullen prime:

[URL="http://primes.utm.edu/primes/page.php?id=87775"]6328548*2^6328548+1 [/URL]

a new Mersenne prime was verified : [url=http://primes.utm.edu/primes/page.php?id=88847]2^42643801-1[/url]!

[QUOTE=kar_bon;177533]a new Mersenne prime was verified : [url=http://primes.utm.edu/primes/page.php?id=88847]2^42643801-1[/url]![/QUOTE]However, we are finding them fast enough, that Caldwell is having trouble keeping up his pages. There are places where he refers to 43 known MP's.

Near Generalized Woodall
 

45444*512^45443-1

[QUOTE=Harvey563;178753]45444*512^45443-1[/QUOTE]

so this is a new entry for [url]http://www.geocities.com/harvey563/NearCullen_WoodallPrimes.txt[/url]

as 11361*2^408989-1 with 123123 digits!

why this prime wasn't found before although the high limit on the above link is given as n=543000!?

so this range only counts for base=2, but not others.
and the special base 512 -> 2^9 makes this prime more harder to find.

so the 'normal' sieve is for (n+1)*2^n-1,
but for a base with power x of 2 someone has to sieve: (n+1)*2^(n*x)-1!?

for example x=10 the sieve/test for n+1 Near Woodall is like:

1001*2^10000-1
1002*2^10010-1
1003*2^10020-1
and so on.

correct? or i'm totally wrong here?

[QUOTE]so this is a new entry for [url]http://www.geocities.com/harvey563/N...dallPrimes.txt[/url][/QUOTE]

No it's not. The link lists "Near-Cullen & Near-Woodall primes" (see the title) considering only base 2, while the reported prime is [U]Generalized[/U] near Woodal, to base 512.

New Near Generalized Woodall
 

80472*256^80473-1 Near Generalized Woodall


Sieved with Rodenkirch's Multisieve.


:hello: