From PrimeGrid....

[quote]World Record Cullen Mega Prime returned
2009-08-01 15:40 UTC
As unbelievable as it may sound, another Cullen Mega Prime has been discovered!!! It is only the 16th known Cullen prime. It is also a top 15 prime at over 2M digits and the largest found by LLR. Additionally, it is PrimeGrid's largest prime to date. The discoverer is from Japan and a member of [URL="http://www.primegrid.com/team_display.php?teamid=194"]Team 2ch[/URL]. Verification is in progress. Stay tuned for more details.
[/quote]

Congrats to Tom [L983] on the new Sophie Germain record!

607095*2^176311-1
607095*2^176312-1

Congrats to David (c4) on the new record Mersenne cofactor:

(2^17683-1)/(234000819833373807217*62265855698776681155719328257)
(5274 digits)

Finding a 29-digit factor 62265855698776681155719328257 of a 5303-digit number is a major factoring achievement!

new GW
 

103444*27^103444-1 Generalized Woodall, ninth largest known.


Steven Harvey

[url=http://primes.utm.edu/primes/page.php?id=91136]27*2^1902689-1[/url]

Good ol' k=27 strikes again.
27*2^627794-1 was my first top-5000 prime, with an entrance rank of 198 that I still haven't beaten.

563528*13^563528-1 is now the biggest GW by far and breaks the base 13 duck at last.

Near-repdigits:
99999993*10^180207-1 180215 L184 Oct 2010 (Near-repdigit)
99999993*10^106947-1 106955 L184 Oct 2010 (Near-repdigit)

The first one is the second largest and missed being the largest by about 30 digits. The second is the 10th largest Near-repdigit.

Larry, congrats on nice primes. I hope you reclaim the NRD record soon.

I stopped all my "side" project a while ago. I found my last NRD more than 3 years ago ...

New record AP4 by Broadhurst - 9,000 digits longer than the previous one! :toot:
[URL]http://primes.utm.edu/primes/page.php?id=95651[/URL]

2^1667321-2^833661+1 (501914 digits) Gaussian Mersenne norm 38

[B]Cruelty[/B]

Congrats on a nice prime!
Can you share exe times, hardware details with us.

Thanks.

Thanks! :smile:
The search runs on single core of C2Q @ 3GHz. Single test using LLR takes ~4800 sec.

2*3^1010743-1 (482248 digits)

k=2 and k=4 @ base=3 tested continouously till n=990k (currently closing a gap till n=1M)

Wow, nice find Cruelty. Do you have a list of primes of this form?
-Curtis

[QUOTE=VBCurtis;270596]Wow, nice find Cruelty. Do you have a list of primes of this form?
-Curtis[/QUOTE]

Look [URL="http://oeis.org/A003307"]here[/URL] and [URL="http://oeis.org/A005540"]here[/URL] :smile:

Congrats to 12121 on a large k=121 prime found jointly with PrimeGrid:

121*2^4553899-1 (1370863 digits)

On 28 Feb 2012, 15:51:22, PrimeGrid’s 27121 Prime Search, through PRPNet and in collaboration with the 12121 Search (k=27 sister project), has found the mega prime: [B][URL="http://primes.utm.edu/primes/page.php?id=105209"]27*2^3855094-1[/URL][/B]
The prime is 1,160,501 digits long and enters Chris Caldwell's [B][URL="http://primes.utm.edu/primes"]The Largest Known Primes Database[/URL][/B] ranked 34th overall. This is PrimeGrid's 23rd mega prime.
The discovery was made by [B]Pietari Snow[/B] of Finland. More details and official announcement to come.



On 28 Feb 2012, PrimeGrid’s Primorial Prime Search, through PRPNet, has found a world record primorial prime: [B][URL="http://primes.utm.edu/primes/page.php?id=105273"]1098133#-1[/URL][/B]
The prime is 476,311 digits long and enters Chris Caldwell's [B][URL="http://primes.utm.edu/primes"]The Largest Known Primes Database[/URL][/B] ranked 1st for Primorial primes and 253rd overall.
The discovery was made by [B]James P. Burt[/B] of the Cayman Islands. More details and official announcement to come.
Congratulations Beyond!!!

Primorials
 

Yes, indeed, special congrats to Beyond for the new Primorial record! I think it takes time to test these numbers, and there are not so many of them. For almost 10 years, 2001-2010 not a single primorial prime was found!

[url]http://primes.utm.edu/top20/page.php?id=5[/url]

12 of top-20 primorials were found by Dubner, including two found in 1984, more than 27 years ago!

Congrats to Curtis on a nice Sophie-Germain pair, currently ranked 15th.

133603707*2^100013-1
133603707*2^100014-1

[QUOTE=Kosmaj;299772]Congrats to Curtis on a nice Sophie-Germain pair, currently ranked 15th.

133603707*2^100013-1
133603707*2^100014-1[/QUOTE]

Thanks! I tested one sieve (n=85001) to k=1G, and then sieved a new file from k=1 to k=2G; I found this pair after less than 5% of the file was tested. Slow going, since I'm using an Atom netbook for the newpgen work!
-Curtis

World Record GFN Prime Found...Twice!
 

[quote]Just prior to the start of the Alan Turing Year Challenge challenge, not one, but two GFN mega primes were found! When all is finalized, these will be the 11th and 12th largest primes found to date and will be the two largest primes found by PrimeGrid. These are each incredible finds!

Internal verification of these primes is ongoing, and for primes of this size will take a few days. Stay tuned for the official announcement.

There's still more than half of the challenge to go...Let's see if we can make it three (or more)! :)
[/quote]

[url]http://www.primegrid.com/forum_thread.php?id=4426[/url]

On 8 Aug 2012, 8:58:58 UTC, PrimeGrid’s Generalized Fermat Prime Search found the [B]largest known Generalized Fermat[/B] mega prime:
[B][URL="http://primes.utm.edu/primes/page.php?id=108818"]475856^524288+1[/URL][/B]

The prime is 2,976,633 digits long and enters Chris Caldwell's [B][URL="http://primes.utm.edu/primes"]The Largest Known Primes Database [/URL] ranked 1st[/B] for Generalized Fermat primes and [B]11th overall[/B].

The discovery was made by [B]Masashi Kumagai[/B] ([URL="http://www.primegrid.com/show_user.php?userid=151189"][B]ragnarag[/B][/URL]) of Japan using an NVIDIA GeForce GTS 450 in an AMD FX(tm)-8150 CPU with 8GB RAM, running 64 bit Windows 7. This GPU took 7 hours 47 minutes to probable prime (PRP) test with GeneferCUDA. Masashi Kumagai is a member of the [B][URL="http://www.primegrid.com/team_display.php?teamid=194"]Team 2ch[/URL][/B] team.

The prime was verified by [B]Jason Preszler[/B] ([B][URL="http://www.primegrid.com/show_user.php?userid=46245"]Jason Preszler[/URL][/B]) of the United States using an Intel Core i7-2600 CPU @ 3.40GHz with 12GB RAM, running 64 bit LINUX . This computer took 46 hours 55 minutes to probable prime (PRP) test with GenefX64. Jason is a member of the [B][URL="http://www.primegrid.com/team_display.php?teamid=1995"]Turan@BOINC[/URL][/B] team.

For more details, please see the [B][URL="http://www.primegrid.com/download/GFN-475856_524288.pdf"]official announcement[/URL][/B].

There's quite a bit of discussion on PG forums how clustered these last three GFNs are. Not unlike the latest Mps.

Congrats to Bishop (L3514) and Primegrid on new largest Fermat divisor:

57*2^2747499+1 (827082 digits)

As a reminder, a prime of form k*2^n+1 can be Fermat divisor with probability 1/k regardless of n.

BTW, the legendary record Fermat divisor found by Cosgrave in 2003 (3*2^2478785+1) is now 3rd!

[QUOTE=Kosmaj;340532]Congrats to Bishop (L3514) and Primegrid on new largest Fermat divisor:

57*2^2747499+1 (827082 digits)

As a reminder, a prime of form k*2^n+1 can be Fermat divisor with probability 1/k regardless of n.

BTW, the legendary record Fermat divisor found by Cosgrave in 2003 (3*2^2478785+1) is now 3rd![/QUOTE]


This is not listed on [url]www.prothsearch.net/fermat.html[/url] yet.
Such results surprise me, since I expect that simple multiplication of 2 numbers of this size should last years. There must be technique I am not aware of.
It is not written what Fermat number has this divisor, but for sure we even cannot imagine the size of this Fermat number.

Congrats to Batalov on nice primes based on known Mersenne primes:

507568*(2^1398269-1)+1, 420927 digits
374568*(2^3021377-1)+1, 909531 digits

BTW, there seems to be a way to include the helper with your submission,
so that the verification on CC's server is done using the helper. See here:
[url]http://primes.utm.edu/primes/page.php?id=115087[/url]

Well, [URL="http://primes.utm.edu/primes/page.php?id=115540"]here's a prime[/URL] that is easy to write down.
It is a "one", followed by 1,059,002 "nines".

Full size posters are available from primes'Я'us.ru ;-)

Congratulations!!!!

There's a large Riesel Problem prime in verification.
It will come in [URL="http://primes.utm.edu/primes/page.php?id=115858"]in position #23[/URL]. Congrats to PGrid!

And a day later, [URL="http://primes.utm.edu/primes/page.php?id=115875"]one more[/URL], also in position #23. ;-)

Yeah, one more:
[URL="http://primes.utm.edu/primes/page.php?id=115875"]304207*2^6643565-1[/URL] (1999918 digits)

Only 82 digits shy of 2M digits!
That's that guy Randy who joined prime search in June this year and already has more than 500 primes in Top-5000, is first by number, and with this one will probably become 11th by score. Amazing computing power! :shock:

Batalov found [url]http://primes.utm.edu/primes/page.php?id=116472[/url]. Congratulations!

Yeah, indeed congrats to Batalov.

And a great chance for the new Fermat divisor record!

[url]http://primes.utm.edu/primes/page.php?id=116744[/url]

A huge [URL="http://primes.utm.edu/primes/page.php?id=116922"]Proth prime[/URL] was found by Tang&PrimeGrid.
I wonder if they are [I]still[/I] in the process of running the xGF tests.

(They should have parallelized them into a lot of "foreach i (2 3 5 6 10 12) pfgw -gos$i -lgos$i.log p" processes. For a plainly run "pfgw -gxo p" result, they may wait for days/weeks. It is also possible to write a parallel implementation, based on the PRP test in Prime95: just a few lines need to be changed and then a GF-divisor test could have been be run threaded, i.e. much faster still.)

Found a couple small "EQ" (Eisenstein-Mersenne cofactors, OEIS [URL="http://oeis.org/A125743"]A125743[/URL]/[URL="http://oeis.org/A125744"]4[/URL]) (probable) primes:
(3^152809+3^76405+1)/7 is a 2-PRP!
(3^272141-3^136071+1)/7 is a 2-PRP!
(3^505823+3^252912+1)/7 is a 2-PRP! (241339 digits)
(3^1353449-3^676725+1)/7 is a 2-PRP! (645759 decimal digits) [B]Time: 10953.669 sec.[/B]

Notes:
1. The running time. With most tools you will get > 20000 sec. This is because of the implementation of FFT modulo 3[SUP]3p[/SUP]+1 with only final step done modulo N.
2. All of similar (composite or prime) numbers are 3-PRPs. Re-validating now with -b5, -b11.

Small prime, but for me it is huge :)

[URL="http://primes.utm.edu/primes/page.php?id=117862"]Fifth in his class in the world[/URL] (currently) of course :))

94 followed but 466002 number nine :)

The Riesel Problem: one less to go
 

A new elimination from the Riesel Problem is currently in the [URL="http://primes.utm.edu/primes/page.php?id=118583"]UTM queue[/URL] (into position 20!)

Congrats to PrimeGrid!

[QUOTE=Batalov;384236]A new elimination from the Riesel Problem is currently in the [URL="http://primes.utm.edu/primes/page.php?id=118583"]UTM queue[/URL] (into position 20!)

Congrats to PrimeGrid![/QUOTE]

Another one!
502573*2^7181987 - 1 is prime!:smile:
Congrats to PrimeGrid.

[URL]http://primes.utm.edu/primes/page.php?id=118597[/URL]
Congratulations to my teammate!

99*10^303255-1 is prime! (303257 decimal digits, P = 33) Time : 2119.757 sec. :smile:

Hi Pepi

Congrats, but it seems it's not enough for top 20 near-repdigits:
[URL="http://primes.utm.edu/top20/page.php?id=15"]http://primes.utm.edu/top20/page.php?id=15[/URL]

[QUOTE=Kosmaj;401394]Hi Pepi

Congrats, but it seems it's not enough for top 20 near-repdigits:
[URL]http://primes.utm.edu/top20/page.php?id=15[/URL][/QUOTE]

I know that fact, but it is rare prime :)
Hunting is continued :)

Last was not in Top 5000 , but this fellow is :)

92*10^544905-1 is prime! (544907 decimal digits, P = 5) Time : 7082.969 sec.

Reported and verified on Top 5000 :)

[QUOTE=pepi37;402390]Last was not in Top 5000 , but this fellow is :)

92*10^544905-1 is prime! (544907 decimal digits, P = 5) Time : 7082.969 sec.

Reported and verified on Top 5000 :)[/QUOTE]

Congrats. That is a lot of nines in its decimal expansion :smile:

[QUOTE=paulunderwood;402392]Congrats. That is a lot of nines in its decimal expansion :smile:[/QUOTE]

Yes, 544905 nines :)

[QUOTE=pepi37;402393]Yes, 544905 nines :)[/QUOTE]

[CODE]? 92*10^1-1
919
? 92*10^2-1
9199
[/CODE]

So there is actual one more: 544906 nines :smile:

Hi Pepi,

Contrats on a nice prime!

[QUOTE=paulunderwood;402394][CODE]? 92*10^1-1
919
? 92*10^2-1
9199
[/CODE]So there is actual one more: 544906 nines :smile:[/QUOTE]


If you count first nine, then it is 544906 :)
But if you say 92....999 then it has 544905 :)

[QUOTE=Kosmaj;402403]Hi Pepi,

Contrats on a nice prime![/QUOTE]

Thanks :)))

Primegrid found huge prime!
[URL]http://primes.utm.edu/primes/page.php?id=120038[/URL]

[B]3 *2^11895718-1[/B] (3580969 digits)

Small but sweet :)

98*10^301354-1 is prime! (301356 decimal digits, P = 4) Time : 1254.194 sec.

MEGA NEAR REPDIGIT PRIME !

After 2.5 years of searching

[URL]http://primes.utm.edu/primes/page.php?id=122228[/URL]

9*10^1009567-1 is prime!

899999999999999...................9

:party: :party: :party:

Congrats :banana:

[QUOTE=paulunderwood;443012]Congrats :banana:[/QUOTE]
Thanks! :smile:

I found a Sophie Germain pair:
73378515705 · 2[SUP]133148[/SUP] - 1
73378515705 · 2[SUP]133147[/SUP] - 1

Congrats :toot:

Congrats to Serge for two Sophie Germain pairs:

10429091973*2^135135-1
10429091973*2^135136-1

13375563435*2^137136-1
13375563435*2^137137-1

:toot:

And another near-repdigit prime

[URL]http://primes.utm.edu/primes/page.php?id=124582[/URL]

92*10^833852-1 is prime!

:bow wave:

31521*2^1778899-1 (before 3 years) and today 663251*2^1778899+1 :)

And today



84256*3^1778899+1 is prime! (848756 decimal digits) Time : 1329.140 sec.

After day and half
45472 *3^1778899-1 is prime!
:smile:
Now I have "pair" on base 2 and base 3
Hunt for primes on base 5 has started :smile:

Verification of new mega repdigit prime is started :)
But I am pretty sure it will be confirmed :)

[URL]https://primes.utm.edu/primes/page.php?id=125948[/URL]


93 · 10^[SUP]1029523[/SUP]-1 is prime :smile:

:party:
After nearly 2.5 years from my last mega ( also ) near-repdigit prime :smile:


From last mega prime to this mega prime I process only 9284 candidates :)
If we take some average number of candidates for one mega prime (38000 on 1e15 as sieve depth) , I was very lucky since I found two in this range.

[QUOTE=pepi37;507061][URL]https://primes.utm.edu/primes/page.php?id=125948[/URL]


93 · 10^[SUP]1029523[/SUP]-1 is prime :smile:

:party:
After nearly 2.5 years from my last mega ( also ) near-repdigit prime :smile:


From last mega prime to this mega prime I process only 9284 candidates :)
If we take some average number of candidates for one mega prime (38000 on 1e15 as sieve depth) , I was very lucky since I found two in this range.[/QUOTE]

Congrats on the occasion of finding a new near-repdigit mega-prime :banana:

[QUOTE=paulunderwood;507161]Congrats on the occasion of finding a new near-repdigit mega-prime :banana:[/QUOTE]

Thanks :smile:

Congrats Serge and Ryan for the 1,533,936 digit Near-repdigit prime:

[URL="https://primes.utm.edu/primes/page.php?id=126112"]992*10^1533933 - 1[/URL] :banana:

But wait...!

Serge, I will hang myself to the first tree :)
Two primes, again you are convincingly leading in this class: but as I know you and Propper you will not stop here....


But on the other hand, I cannot beat those computer resources Propper have, so I must reconcile with destiny , and I must know what is my limits :))


Congratulations!

[QUOTE=Batalov;508606]But wait...![/QUOTE]

[URL="https://primes.utm.edu/primes/page.php?id=126113"]99*10^1536527-1 is prime![/URL]

Congrats Serge and Ryan for this second Near-redigit prime. :banana:

Congratulations!
:tu:
[QUOTE=Batalov;508606]But wait...![/QUOTE]
Oh, goody! This is [i]way[/i] better than the "there's more!" promised in [strike]scammercials[/strike] infomercials.

I did notice something weird on the page showing the first of the two newly-discovered megaprimes:[quote]Running N+1 test using discriminant 3,[/quote]But-but-but--- 3 isn't a discriminant! Stickelberger's criterion for the discriminant, you know. The discriminant for Q(sqrt(3))/Q is 12.

Serge and Ryan do it again:

[URL="https://primes.utm.edu/primes/page.php?id=126215"]993*10^1768283 - 1[/URL] :banana:

[QUOTE=paulunderwood;509141]Serge and Ryan do it again:

[URL="https://primes.utm.edu/primes/page.php?id=126215"]993*10^1768283 - 1[/URL] :banana:[/QUOTE]
Verification still "InProcess," but I'm sure that's merely a formality, so congratulations in advance!
:beer2: :beer2:
:party:

[QUOTE=paulunderwood;509141]Serge and Ryan do it again:

[URL="https://primes.utm.edu/primes/page.php?id=126215"]993*10^1768283 - 1[/URL] :banana:[/QUOTE]
I will always be second on third or 15 on the list :)

last time they go together they stopped at 5.2 M digits :))


But in any way, congratulations!

Nice job!
Congrats :party:

Speaking of other primes - Peter Kaiser's latest Quad is out there in outer space!
[url]https://primes.utm.edu/top20/page.php?id=55[/url]

[B]10,132 digits! [/B]

This quad has a remarkably high difficulty level! Congratulations to Peter!

Thanks!
I am still trying to decide what to go for next. So many ideas but they are all probably too hard...

Every section of the specialized Top 20s is interesting in its own way. Breaks the monotony!

Try maybe Irregular primes (both kinds)*, ...maybe Generalized Lucas primitive part, maybe something else? They all need different attacks. All are interesting in their own way.
Well, except some categories :-) Some are just - "plan for a certain number of hours, and you will be done with the next sequence member". For example partition numbers. I am pretty sure that these could be in and out. I found an interesting twist for myself there trying to find a large prime partitions(n^2), and I did; there are no easy others. Maybe someone can find a large prime partitions(n^3)? (though I have probably already tried. I don't remember off the top of my head).

____________________
*That would be a lot of ECM; with a specific challenge: it is not documented anywhere how far [I]others [/I]already ECMd. These are rather very refractory to attempts, in my experience.

The Fibonacci PRPs [URL="https://primes.utm.edu/top20/page.php?id=39"]U(130021) and U(148091)[/URL] are ripe for a multi-core Primo proof. Alternatively, there are some smaller Mersenne co-factors that need proofs.

Congrats for your latest quadruplet.

[QUOTE=paulunderwood;509527]The Fibonacci PRPs [URL="https://primes.utm.edu/top20/page.php?id=39"]U(130021) and U(148091)[/URL] are ripe for a multi-core Primo proof. Alternatively, there are some smaller Mersenne co-factors that need proofs.

Congrats for your latest quadruplet.[/QUOTE]

I'll take on one of the mersenne cofactors; is there a place where some proofs are reserved, or a list of which need primo proofs?

[QUOTE=VBCurtis;509537]I'll take on one of the mersenne cofactors; is there a place where some proofs are reserved, or a list of which need primo proofs?[/QUOTE]

Those on [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282%5Ep-1%29%2Fn&action=Search"]this list[/URL] but not on [URL="https://primes.utm.edu/top20/page.php?id=49"]this one[/URL]. I recommend at least 16 cores :wink:

I don't know about coordination. HTH.

Speaking about primo proofs:

I have a few (4 + 2) candidates of [URL="https://primes.utm.edu/top20/page.php?id=26"]irregular[/URL] and [URL="https://primes.utm.edu/top20/page.php?id=25"]Euler irregular[/URL] primes waiting for a primo primality proof.

They are ranging from about 22000 to 29000 digits, but are far beyond my current computing resources.

If one of you is (seriously) interested, please drop me a note.

[QUOTE=Batalov;509446]Speaking of other primes - Peter Kaiser's latest Quad is out there in outer space!
[url]https://primes.utm.edu/top20/page.php?id=55[/url]

[B]10,132 digits! [/B]

This quad has a remarkably high difficulty level! Congratulations to Peter![/QUOTE]

Congratulations. It is truly impressive! Over twice the number of digits than the previous one (5003 digits on March 2016).

A new Generalized Fermat has been found
2733014[SUP]524288[/SUP] + 1
While not the largest Generalized Fermat it is (by far) the largest prime for [B]2019[/B] with ‎3'374,655 digits.

Congratulations to Yair Givoni and [URL="http://www.planetary.org/"]The Planetary Society.[/URL]

4 primes in Arithmetic Progresison
 

2 Sets
Largest examples for an AP-4


a) 1027676400 · 60013# + 1 (4th term) 25992 digits

b) 1025139165 · 60013# + 1 (4th term) 25992 digits

By Ken J. Davis

Congratulations!

new Generalized Woodall
 

321671*34^321671-1 (492638 digits) is the ninth largest known Generalized Woodall prime, and the ninth known prime of the form n*34^n-1.

A new Generalized Fermat has been found
2788032[SUP]524288[/SUP] + 1
While not the largest Generalized Fermat it is the largest prime for [B]2019[/B] with 3'379,193 digits.

Congratulations to user "Sheep"

Sexy primes
 

Congrats to GEN-ERIC for the primes [p,p+6] = (18041#/14*2^39003-4)±3.

[url]http://primepairs.com/[/url]

[QUOTE=paulunderwood;514161]Congrats to GEN-ERIC for the primes [p,p+6] = (18041#/14*2^39003-4)±3.

[url]http://primepairs.com/[/url][/QUOTE]
Congrats! However, that's a strange website with weak, incorrect statements.
[QUOTE=http://primepairs.com/]...breaking the prior record of 11,593 digits which, according to Wikipedia, had stood for nearly a decade.[/QUOTE]
What about 6521953289619 * 2^55555 - 5 and [URL="https://primes.utm.edu/primes/page.php?id=114018"]6521953289619 * 2^55555 + 1[/URL] (16737d) dated Apr 2013?
Should one think that Peter immediately rushes to Wikipedia to update his record for posterity after finding a record? I am sure that he has other better things to do. Or maybe someone else does for him? Also probably not.

There is a reason why even school teachers don't give children a grade for a quote from Wiki. Wiki is broadly correct in generalities, and overwhelmingly incorrect in expert details.
The algorithm for searching for facts is: start with a general blurp from Wikipedia, continue searching using links and links from links... then you might build some semblance of a current state of the art.

[QUOTE=Batalov;514163]Congrats! However, that's a strange website with weak, incorrect statements.

What about 6521953289619 * 2^55555 - 5 and [URL="https://primes.utm.edu/primes/page.php?id=114018"]6521953289619 * 2^55555 + 1[/URL] (16737d) dated Apr 2013?
Should one think that Peter immediately rushes to Wikipedia to update his record for posterity after finding a record? I am sure that he has other better things to do. Or maybe someone else does for him? Also probably not.

There is a reason why even school teachers don't give children a grade for a quote from Wiki. Wiki is broadly correct in generalities, and overwhelmingly incorrect in expert details.
The algorithm for searching for facts is: start with a general blurp from Wikipedia, continue searching using links and links from links... then you might build some semblance of a current state of the art.[/QUOTE]

I'd argue Peter's triplet is not so sexy since there is a prime at 6521953289619 * 2^55555 - 1 :boxer:

On the other hand:

[QUOTE]Prime pairs with a prime gap of 6 are known as sexy primes (p, p+6).
e.g., (5, 11), (7, 13), (11, 17), (13, 19), (17, 23), etc. [/QUOTE]

there is a prime between 17 and 23 :down:

[QUOTE=paulunderwood;514161]Congrats to GEN-ERIC for the primes [p,p+6] = (18041#/14*2^39003-4)±3.

[url]http://primepairs.com/[/url][/QUOTE]

That is just painful. I mean the ecpp proof for the hard number when you have a much cheaper way, searching a better form.

Say
2^a divides p-1
3^b divides p+5

ofcourse you want 2^a~3^b (~sqrt(N)) because then you know large p-1,(p+6)-1 factors in the oder of sqrt(N), so

a=floor(log(N)/log(2)/2)
b=floor(log(N)/log(3)/2)

you can search p in the form (because 2^a and 3^b are coprime):

p=u*2^a+v*3^b,
from divisibilities you can get:

[CODE]
v*3^b==1 mod 2^a
u*2^a==-5 mod 3^b
[/CODE]

Don't need to run two variables, fix u, then run v in arithmetic progression. Use sieving.

[QUOTE=R. Gerbicz;514165]That is just painful. I mean the ecpp proof for the hard number when you have a much cheaper way, searching a better form.

Say
2^a divides p-1
3^b divides p+5

ofcourse you want 2^a~3^b (~sqrt(N)) because then you know large p-1,(p+6)-1 factors in the oder of sqrt(N), so

a=floor(log(N)/log(2)/2)
b=floor(log(N)/log(3)/2)

you can search p in the form (because 2^a and 3^b are coprime):

p=u*2^a+v*3^b,
from divisibilities you can get:

[CODE]
v*3^b==1 mod 2^a
u*2^a==-5 mod 3^b
[/CODE]

Don't need to run two variables, fix u, then run v in arithmetic progression. Use sieving.[/QUOTE]

Somebody, maybe GEN-ERIC with his 16 core Threadripper, should try to beat his record with the above method: The gauntlet has been thrown down!

[QUOTE=R. Gerbicz;514165]That is just painful. I mean the ecpp proof for the hard number when you have a much cheaper way, searching a better form.

Don't need to run two variables, fix u, then run v in arithmetic progression. Use sieving.[/QUOTE]
Exactly! This new thingy completely misses the precious beauty of [URL="https://groups.yahoo.com/neo/groups/primenumbers/conversations/topics/20207"]Ken Davis' construction[/URL].
Surely now, 10 years later, one can repeat Ken's trick to find a couple 40,000-digit sexy primes.

I added a little [URL="https://mersenneforum.org/showthread.php?t=24317"]friendly competition thread[/URL]. Have some fun!

[QUOTE=paulunderwood;514164]I'd argue Peter's triplet is not so sexy since there is a prime at 6521953289619 * 2^55555 - 1 :boxer:
On the other hand:
there is a prime between 17 and 23 :down:[/QUOTE]


YepI And that is what we call a triplet, which -at least for large enough numbers- is more important than just a pair of sexy primes. 😋

[QUOTE=paulunderwood;514161]Congrats to GEN-ERIC for the primes [p,p+6] = (18041#/14*2^39003-4)±3.

[URL]http://primepairs.com/[/URL][/QUOTE]
Well, that world record didn't live long...

A new Cunningham Chain of the 2[SUP]nd[/SUP] kind was published a few days ago.

Congratulations to Serge Batalov on the record. (2p+1)

556336461 · 2[SUP]211356[/SUP] - 1 with 63634 Digits [URL="https://primes.utm.edu/primes/page.php?id=126495"]HERE[/URL]

The previous record had 52726 digits.

Congrats to Ryan for a [URL="https://primes.utm.edu/primes/page.php?id=129914"]top20 prime[/URL] 7*6^6772401+1 (5269954 digits) :banana: