Other Primes

[Trying2Sieve]

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]

P1174253 was proven prime using PFGW 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.

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

The decimal integer can be generated in PARI/GP 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.

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");
\\\\\\

The file P1174253.txt contains the decimal integer.
Thank you for your time.

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

Credits and thanks to George, Mark, PFGW and PARI/GP.

[a1call]

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.

[bur]

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]

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]

Originally Posted by a1call

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.

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

[a1call]

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]

Please see attached a pfgw-prime.log 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), iterating on the larger twin prime. The largest I found are 3049 dd. It's abandoned, so anyone is welcome to continue if they wish.

[lastest00]

How to post new digit primes, n achieve reward?

[paulunderwood]

Congrats to Roman Trunov and Brian D. Niegocki for the (GFN based) Cunningham Chain 893962950^16384+1 and 2*893962950^16384+1, at 146,659 digits smashing the previous record of 77,078 digits.

[Cybertronic]

Originally Posted by paulunderwood

Congrats to Roman Trunov and Brian D. Niegocki for the (GFN based) Cunningham Chain 893962950^16384+1 and 2*893962950^16384+1, at 146,659 digits smashing the previous record of 77,078 digits.

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