288465! + 1
 

Congrats to René Dohmen for the new [URL="https://primes.utm.edu/primes/page.php?id=133139"]factorial prime 288465! + 1[/URL] (1,449,771 decimal digits) :banana:

Seems that this prime was found outside of [URL="http://prpnet.primegrid.com:12002/"]Factorial Prime Search[/URL] by Primegrid.

[QUOTE=unconnected;597601]Seems that this prime was found outside of [URL="http://prpnet.primegrid.com:12002/"]Factorial Prime Search[/URL] by Primegrid.[/QUOTE]

Sniped! :snipe:

Time to update
[url]https://oeis.org/A002982[/url]:smile:

[QUOTE=rudy235;597612]Time to update
[url]https://oeis.org/A002982[/url]:smile:[/QUOTE]

I think you mean [url]https://oeis.org/A002981[/url]?

[QUOTE=mathwiz;597627]I think you mean [url]https://oeis.org/A002981[/url]?[/QUOTE]

Exactly! N! + 1
I misread the post.

New factorial prime
 

A new factorial prime was [URL="https://primes.utm.edu/primes/page.php?id=133139"]recently reported[/URL] (not yet validated):

288465! + 1

It is very close to the PRPnet search wavefront, is that a coincidence?

Congrats to PrimeGrid for the [URL="https://primes.utm.edu/primes/page.php?id=133193"]"321" prime 3*2^18196595 - 1[/URL] (5,477,722 decimal digits, rank 20) :banana:

Sniped again! Congrats to Ryan Propper for the [URL="https://primes.utm.edu/primes/page.php?id=133196"]factorial prime 308084! + 1[/URL] (1,557,176 decimal digits) :banana:

Great to see such progress on the Factorials. Apparently there were so few over the years because few people were working on them. I still think it'd be nice if the work was organized so ranges aren't done twice or thrice, which might well be the case now.

[QUOTE=bur;598421]Great to see such progress on the Factorials. Apparently there were so few over the years because few people were working on them. I still think it'd be nice if the work was organized so ranges aren't done twice or thrice, which might well be the case now.[/QUOTE]

Don't know who else out there is working on these, but I've sieved (and plan to test) n! ± 1 for 300,000 <= n <= 500,000.

Update: I've completed testing/double-checking [$]n!-1[/$] and [$]n!+1[/$] for [$]150000 \le n \le 330000[/$] and can confirm the only primes are the 4 [URL="https://primes.utm.edu/top20/page.php?id=30"]known[/URL] as of Jan 2022:

[CODE]308084! + 1
288465! + 1
208003! - 1
150209! + 1[/CODE]

Continuing on up to [$]n=500000[/$].

[QUOTE=ryanp;599226]Update: I've completed testing/double-checking [$]n!-1[/$] and [$]n!+1[/$] for [$]150000 \le n \le 330000[/$] and can confirm the only primes are the 4 [URL="https://primes.utm.edu/top20/page.php?id=30"]known[/URL] as of Jan 2022:

[CODE]308084! + 1
288465! + 1
208003! - 1
150209! + 1[/CODE]

Continuing on up to [$]n=500000[/$].[/QUOTE]

I suppose that PrimeGrid's factorial sub-project is defunct now, unless they start at n=500000 :wink:

Update: search limit for [$]n! ± 1[/$] is now at [$]n=400000[/$].

New [URL="https://primes.utm.edu/primes/page.php?id=133604"]factorial prime[/URL] from Mr. Propper, this will take a while to verify.

Will there ever be an Official Announcement?
 

[QUOTE=paulunderwood;598299]Congrats to PrimeGrid for the [URL="https://primes.utm.edu/primes/page.php?id=133193"]"321" prime 3*2^18196595 - 1[/URL] (5,477,722 decimal digits, rank 20) :banana:[/QUOTE]

.
[QUOTE]6 3*2^18196595-1 5,477,722 (decimal) vaclav_m (primes) BOINC@Poland 2022-01-08 20:46:05 UTC T5K [C]No official Announcement[/C] 321 Prime Search 217,652.558[/QUOTE]

Another [URL="https://primes.utm.edu/primes/page.php?id=133776"]321- prime![/URL]:3 *2^18924988-1 This one with 5,696,990 and entrance rank 18. So soon after the previous one. :smile:

2^64 - 189
 

I found 2 large primes with coefficients (2^64 - 189) then 000000 (like 500,000 rep units) followed by a 1.

Was a long time ago though.

P1174253
 

[B]P1174253 [/B]was proven prime using [B]PFGW [/B]on Christmas eve 2022.
Please see the attached screenshots and the files used to run the proof.
The proof testing was done by placing the following 3 files in the PFGW folder and running the batch file on a windows system.

[B]ETP-100-A-1run-proof.bat[/B] (Batch file)
[B]ETP-110-A-pfgw-prime.txt[/B] (helper file)
[B]ETP-120-A-b.txt[/B] (Candidate to test)

The decimal integer can be generated in [B]PARI/GP[/B] by the following code, however the screen buffer will run out while "printing" the 1174253 decimal digits of the integer.
You can insteat use the "write" command to print the entire digits to a file.

[CODE]k = [1, 1, 1, 2, 5, 9, 6, 79, 16, 219, 580, 387, 189, 7067, 1803, 6582, 31917, 18888, 20973, 132755, 11419, 50111];
q = 2;
for(i=1, #k, q = k[i]*(q-1)*q+1);
print("\n",q,"\n");
\\\\\\
[/CODE]

The file [B]P1174253.txt[/B] contains the decimal integer.
Thank you for your time.

[url]https://primes.utm.edu/primes/page.php?id=134690[/url]

Credits and thanks to [B]George, Mark, PFGW and PARI/GP[/B]. :smile:

I think i have an unusual setup. Please see the attached screenshots of the next iteration in progress.
FTR and in the unlikely case, anyone would find it useful:
* I have a windows-guest VirtualBox virtual machine on a 16 core Ryzen 9 desktop.
* I use one instance of PARI-GP to continuously sieve a given k-range using gcd
* Multiple instances of PARI-GP read remaining k's using the system command, generate a PFGW short PRP script and invoke PFGW using the system command and move to next remaining k when done
* I have a series of DOS batch files which automate the above processes.

Thank you for your time. :smile:

I noticed that prime when it appeared at Caldwell's list. It seems to be constructed like Euclid numbers but modified with that list of k's. How were these values decided?

Hi bur,
1st value of small Prime q (2 in this case) is a random choice.
Every k is the smallest value that will yield a Prime for each iteration. This way, all the Prime factors of N-1 (for all iterations) are known as long as all k’s are small enough to be fully factored.

[QUOTE=a1call;622925]Hi bur,
1st value of small Prime q (2 in this case) is a random choice.
Every k is the smallest value that will yield a Prime for each iteration. This way, all the Prime factors of N-1 (for all iterations) are known as long as all k’s are small enough to be fully factored.[/QUOTE]

Are you aware of what work has gone into other starting numbers?

No, I’m not. I have tried a N+1 version and a twin Prime version, but I decided to concentrate on the above version. Anyone is welcome to pursue their own attempts.

Please see attached a [B]pfgw-prime.log[/B] file which can be used as a helper file (editing required) for twin prime search (the smaller Twin-Prime not required for the helper file), [B]iterating on the larger twin prime[/B]. The largest I found are [B]3049 dd[/B]. It's abandoned, so anyone is welcome to continue if they wish. :smile:

How to post new digit primes, n achieve reward?

CC2
 

Congrats to Roman Trunov and Brian D. Niegocki for the (GFN based) Cunningham Chain [URL="https://primes.utm.edu/primes/page.php?id=135153"]893962950^16384+1 [/URL] and [URL="https://primes.utm.edu/primes/page.php?id=135154"]2*893962950^16384+1[/URL], at 146,659 digits smashing the previous record of 77,078 digits.

[QUOTE=paulunderwood;624565]Congrats to Roman Trunov and Brian D. Niegocki for the (GFN based) Cunningham Chain [URL="https://primes.utm.edu/primes/page.php?id=135153"]893962950^16384+1 [/URL] and [URL="https://primes.utm.edu/primes/page.php?id=135154"]2*893962950^16384+1[/URL], at 146,659 digits smashing the previous record of 77,078 digits.[/QUOTE]

Thanks for the information,Paul !
Page was updated: [url]https://www.pzktupel.de/JensKruseAndersen/cc.php[/url]

[QUOTE=paulunderwood;624565]Congrats to Roman Trunov and Brian D. Niegocki for the (GFN based) Cunningham Chain [URL="https://primes.utm.edu/primes/page.php?id=135153"]893962950^16384+1 [/URL] and [URL="https://primes.utm.edu/primes/page.php?id=135154"]2*893962950^16384+1[/URL], at 146,659 digits smashing the previous record of 77,078 digits.[/QUOTE]
It was a nice idea, but not sure what (re-)sieve they used. Sure, they had a well-sieved (and dense) b^16384+1 set from past times, but 2*b^16384+1 (and/or b^16384/2+1, too) had to be sieved, which does not look too fast.

Easier to improve that with a traditional sieve, I would think...
[URL="https://t5k.org/primes/page.php?id=135800"]213778324725*2^561417+1[/URL] (p)
[URL="https://t5k.org/primes/page.php?id=135801"]213778324725*2^561418+1[/URL] (2p-1)

[QUOTE=Batalov;626928]It was a nice idea, but not sure what (re-)sieve they used. Sure, they had a well-sieved (and dense) b^16384+1 set from past times, but 2*b^16384+1 (and/or b^16384/2+1, too) had to be sieved, which does not look too fast.

Easier to improve that with a traditional sieve, I would think...
[URL="https://t5k.org/primes/page.php?id=135800"]213778324725*2^561417+1[/URL] (p)
[URL="https://t5k.org/primes/page.php?id=135801"]213778324725*2^561418+1[/URL] (2p-1)[/QUOTE]

Congrats for the 169,015 digits pair.

Congrats, page was updated !
[url]https://www.pzktupel.de/JensKruseAndersen/cc.php[/url]

New 1.58M near-repdigit is found :)
From last hit in same sequence difference is only cca 8500 candidates :) ( and 2.5 years time difference) :)

And now it is official :)

[URL="https://t5k.org/primes/page.php?id=135919"]https://t5k.org/primes/page.php?id=135919[/URL]

92 ·10^1585996-1

PrimeGrid has just found [URL="https://t5k.org/primes/page.php?id=136240"]3 * 2^20928756 - 1[/URL], 6,300,184 digits long.

After a recent "drive" on crunching 321 candidates to celebrate Blaise Pascal's 400th birthday, Arno Lehmann has found the 19th largest prime to date: [URL="https://t5k.org/primes/page.php?id=136240"]3 *2^20928756-1[/URL] (6,300,184 digits).

:george:

Congratulation to a new rexord Thabit-prime !!!