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paulunderwood 2022-01-10 19:42

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:

unconnected 2022-01-10 22:07

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

paulunderwood 2022-01-10 22:39

[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:

rudy235 2022-01-10 23:30

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

mathwiz 2022-01-11 01:32

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

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

rudy235 2022-01-11 07:32

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

Exactly! N! + 1
I misread the post.

bur 2022-01-11 09:53

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?

paulunderwood 2022-01-18 23:36

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:

paulunderwood 2022-01-20 16:54

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:

bur 2022-01-20 17:54

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.

ryanp 2022-01-20 20:33

[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.

ryanp 2022-02-01 22:23

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 [$]n=500000[/$].

paulunderwood 2022-02-01 22:39

[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:

ryanp 2022-02-11 21:00

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

unconnected 2022-02-22 07:06

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

rudy235 2022-03-16 15:05

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]

paulunderwood 2022-03-27 18:25

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:

Trying2Sieve 2022-12-15 12:09

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.

a1call 2023-01-07 05:43

P1174253
 
3 Attachment(s)
[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:

a1call 2023-01-18 02:10

2 Attachment(s)
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:

bur 2023-01-19 10:26

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?

a1call 2023-01-19 13:39

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.

henryzz 2023-01-20 13:09

[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?

a1call 2023-01-20 14:10

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.

a1call 2023-01-20 17:25

1 Attachment(s)
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:

lastest00 2023-01-29 20:55

How to post new digit primes, n achieve reward?


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