(x)(G)FN Divisibility Testing - a request for help!

xGFN = extended Generalized Fermat Number
We're searching for 3 types of divisors
1. Fermat Number divisors
2. Generalized Fermat Number divisors
3. extended Generalized Fermat Number divisors

The recent Mega Prime (3*2^5082306+1) found in the 321 Prime Search is a Proth prime and thus, we are testing it for (x)(G)FN divisibility. On a single core, this test could take 4 to 6 months to complete. Using certain "shortcuts", we could bring it down to 2 1/2 months.

However, the fastest method, while not the most efficient use of resources, is to split the work up over 42 cores. This would allow for completion in about 5 days. To expedite the testing, we are asking for help.

The software used for testing is openPFGW. It's available for both Linux and Windows. It can be downloaded here: openPFGW

There is no check-pointing for these single tests; therefore, it will need to run uninterrupted to completion.

For Windows users, copy and paste one of the command lines below into the Standard "PFGW compatible" command line field and click start. For Linux users, just start in a terminal and run one of the command lines below.

If you have available resources (P4 3.4GHz, C2D, C2Q, or Phenom or better) and would like to help, please select a test below. This thread will serve as the reservation thread as well. Just post which test you'd like to reserve.

Upon completion of the test, upload the 3_5082306_#.gfi and #_#.log files here. Select upload in the Menu on the top right of the page.

If all goes well and everything is reserved in the next couple of days, we can have this wrapped up within a week. Thank you for your help.

Times are based on a 10-15 hour completion time for an LLR test on 3*2^5082306+1.

40-60 hour tests
pfgw -l2_1.log -gxo2,1 -a2 -q3*2^5082306+1 Benva COMPLETE (none)
pfgw -l3_1.log -gxo3,1 -a2 -q3*2^5082306+1 [SG-SPEG] BerndBrot COMPLETE
pfgw -l5_1.log -gxo5,1 -a2 -q3*2^5082306+1 Puzzle-Peter COMPLETE
pfgw -l6_1.log -gxo6,1 -a2 -q3*2^5082306+1 Puzzle-Peter COMPLETE
pfgw -l7_1.log -gxo7,1 -a2 -q3*2^5082306+1 Puzzle-Peter COMPLETE
pfgw -l8_1.log -gxo8,1 -a2 -q3*2^5082306+1 Sysadm@Nbg COMPLETE
pfgw -l10_1.log -gxo10,1 -a2 -q3*2^5082306+1 [SG-SPEG]SDI COMPLETE (none)
pfgw -l11_1.log -gxo11,1 -a2 -q3*2^5082306+1 gamer007 COMPLETE
pfgw -l12_1.log -gxo12,1 -a2 -q3*2^5082306+1 pschoefer COMPLETE (none)

80-120 hour tests
pfgw -l3_2.log -gxo3,2 -a2 -q3*2^5082306+1 pschoefer COMPLETE
pfgw -l4_3.log -gxo4,3 -a2 -q3*2^5082306+1 Sysadm@Nbg COMPLETE
pfgw -l5_2.log -gxo5,2 -a2 -q3*2^5082306+1 Puzzle-Peter COMPLETE
pfgw -l5_3.log -gxo5,3 -a2 -q3*2^5082306+1 [SG-SPEG]SDI COMPLETE
pfgw -l5_4.log -gxo5,4 -a2 -q3*2^5082306+1 pan2000 COMPLETE
pfgw -l6_5.log -gxo6,5 -a2 -q3*2^5082306+1 [SG-SPEG]Saerdna COMPLETE
pfgw -l7_2.log -gxo7,2 -a2 -q3*2^5082306+1 [SG-SPEG] Yamazaki COMPLETE
pfgw -l7_3.log -gxo7,3 -a2 -q3*2^5082306+1 Scott Brown COMPLETE (none)
pfgw -l7_4.log -gxo7,4 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l7_5.log -gxo7,5 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l7_6.log -gxo7,6 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l8_3.log -gxo8,3 -a2 -q3*2^5082306+1 [SG-SPEG] Yamazaki COMPLETE
pfgw -l8_5.log -gxo8,5 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l8_7.log -gxo8,7 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l9_2.log -gxo9,2 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l9_5.log -gxo9,5 -a2 -q3*2^5082306+1 Mike COMPLETE
pfgw -l9_7.log -gxo9,7 -a2 -q3*2^5082306+1 pschoefer COMPLETE
pfgw -l9_8.log -gxo9,8 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l10_3.log -gxo10,3 -a2 -q3*2^5082306+1 PrimeGrid COMPLETE
pfgw -l10_7.log -gxo10,7 -a2 -q3*2^5082306+1 PrimeGrid COMPLETE
pfgw -l10_9.log -gxo10,9 -a2 -q3*2^5082306+1 [SG]marodeur6 COMPLETE
pfgw -l11_2.log -gxo11,2 -a2 -q3*2^5082306+1 [SG]marodeur6 COMPLETE
pfgw -l11_3.log -gxo11,3 -a2 -q3*2^5082306+1 [SG]marodeur6 COMPLETE
pfgw -l11_4.log -gxo11,4 -a2 -q3*2^5082306+1 [SG]marodeur6 COMPLETE
pfgw -l11_5.log -gxo11,5 -a2 -q3*2^5082306+1 [SG]marodeur6 COMPLETE
pfgw -l11_6.log -gxo11,6 -a2 -q3*2^5082306+1 [SG]marodeur6 COMPLETE
pfgw -l11_7.log -gxo11,7 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l11_8.log -gxo11,8 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l11_9.log -gxo11,9 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l11_10.log -gxo11,10 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l12_5.log -gxo12,5 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l12_7.log -gxo12,7 -a2 -q3*2^5082306+1 Lennart COMPLETE
pfgw -l12_11.log -gxo12,11 -a2 -q3*2^5082306+1 Lennart COMPLETE

GF Results
3*2^5082306+1 is a Factor of GF(5082303,3)!!!! (202011.866000 seconds)
3*2^5082306+1 is a Factor of GF(5082305,5)!!!! (-1238.488832 seconds)
3*2^5082306+1 is a Factor of GF(5082304,8)!!!! (1561.071728 seconds)
3*2^5082306+1 is a Factor of GF(5082305,11)!!!! (205798.451000 seconds)

xGF Results
3*2^5082306+1 is a Factor of xGF(5082305,5,3)!!!! (334860.541000 seconds)
3*2^5082306+1 is a Factor of xGF(5082302,7,4) !!!! (-1447.827456 seconds)
3*2^5082306+1 is a Factor of xGF(5082304,8,3)!!!! (319349.797000 seconds)
3*2^5082306+1 is a factor of xGF(5082305,8,5)!!!! (1529.506816 Seconds)
3*2^5082306+1 is a Factor of xGF(5082305,9,5)!!!! (1733.716816 seconds)
3*2^5082306+1 is a Factor of xGF(5082304,9,8)!!!! (-942.306640 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,11,3)!!!! (281658.843000 seconds)
3*2^5082306+1 is a Factor of xGF(5082302,11,5)!!!! (299775.602000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,11,8)!!!! (800.930656 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,11,9)!!!! (715.380656 seconds)
3*2^5082306+1 is a Factor of xGF(5082303,12,7)!!!! (754921.205000 seconds)

A GF Factor was found, but the base of 5082274 may not be correct.
3*2^5082306+1 is a Factor of xGF(5082274,3,2)!!!! (389561.594000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,4,3)!!!! (-2051.731696 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,5,2)!!!! (425216.233000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,5,4)!!!! (579596.208000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,6,5)!!!! (443921.688000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,7,2)!!!! (286408.437000 seconds)
3*2^5082306+1 is a factor of xGF(5082274,7,5) !!!! 1209.948912 seconds
3*2^5082306+1 is a factor of xGF(5082274,7,6) !!!! (151.113360 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,8,7)!!!! (1900.356816 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,9,2)!!!! (1814.426816 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,9,7)!!!! (287682.716000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,10,3)!!!! (391912.438000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,10,7)!!!! (391940.578000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,10,9)!!!! (486428.766000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,11,2)!!!! (489581.705000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,11,4)!!!! (281660.359000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,11,6)!!!! (440029.000000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,11,7)!!!! (-726.596640 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,11,10)!!!! (750482.487000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,12,5)!!!! (755207.783000 seconds)
3*2^5082306+1 is a Factor of xGF(5082274,12,11)!!!! (375898.531000 seconds)
____________

Hi John,

after some 48 hours my 1. file seemed to be finished...
(pfgw -l7_2.log -gxo7,2 -a2 -q3*2^5082306+1)

but then it started again for a second run...
is that ok ?

regards

The second run is needed. The 80-120 hour tests actually have two runs...one for each power.

My personal forecast sees
- the short GFN-test at 98 hours
- the long at 97 hours, but if there is a second run, it will be at ~190 hours

My machine:
AMD Phenom 9550 running Ubuntu Linux 64-bit

I ve finished my range, but I have no 3_5082306_#.gfi file and #_#.log is empty, is it normal?

Reserving the last one
pfgw -l9_7.log -gxo9,7 -a2 -q3*2^5082306+1
pschoefer
ETA: 13 Apr

Using the results that are coming in, there are 3 possible outcomes:

1. Log file is empty.
   
2. Log file has a factor.
   3*2^5082306+1 is a Factor of GF(5082303,3)!!!! (202011.866000 seconds)
   
3. Log file has a message & a factor.
   A GF Factor was found, but the base of 5082274 may not be correct.
   3*2^5082306+1 is a Factor of xGF(5082274,7,2)!!!! (286408.437000 seconds)
   

It is important to know which outcome it is. So far, so good.

Thank you!
____________

I'm getting the impression that several tasks running on the same machine slow each other down. Anybody else experiencing the same?

I'm getting the impression that several tasks running on the same machine slow each other down. Anybody else experiencing the same?

I'm getting the impression that several tasks running on the same machine slow each other down. Anybody else experiencing the same?

Might be an issue with the shared L2 cache, since core0 and core1 are using the same cache.

Sadly, we are experiencing the same...and we also suspect L2 cache. We notice a 50% decrease in speed if more than 2 tests are being run on a quad.

So I'm really sorry to tell you, that i have 8 test parallel on my V8 :(

I'm very sorry for that but the estimated deadline for the first run will be in 5 days... And there will be a second run as I have read here. So overall I will need 17 days from today to finish this 8 Test.

What's all this "but the base of 5082274 may not be correct" business? How do we (you) determine whether a factor has been found or not?
____________
There are only 10 kinds of people - those who understand binary and those who don't

What's all this "but the base of 5082274 may not be correct" business? How do we (you) determine whether a factor has been found or not?

A GF Factor was found, but the base of 5082274 may not be correct.
3*2^5082306+1 is a Factor of xGF(5082274,11,10)!!!! (750482.487000 seconds)

PFGW -gxoq -a2
3*2^5082306+1 is a Factor of GF(5082305-? ,3)!!!!
3*2^5082306+1 is a Factor of GF(5082305,5)!!!!
3*2^5082306+1 is a Factor of xGF(5082305,5,3)!!!!
3*2^5082306+1 is a Factor of xGF(5082305-? ,7,4)!!!!
3*2^5082306+1 is a Factor of GF(5082305-? ,8)!!!!
3*2^5082306+1 is a Factor of xGF(5082305-? ,8,3)!!!!
3*2^5082306+1 is a Factor of xGF(5082305,8,5)!!!!
3*2^5082306+1 is a Factor of xGF(5082305,9,5)!!!!
3*2^5082306+1 is a Factor of xGF(5082305-? ,9,8)!!!!
3*2^5082306+1 is a Factor of GF(5082305,11)!!!!
3*2^5082306+1 is a Factor of xGF(5082305,11,3)!!!!
3*2^5082306+1 is a Factor of xGF(5082305-? ,11,5)!!!!
3*2^5082306+1 is a Factor of xGF(5082305,11,8)!!!!
3*2^5082306+1 is a Factor of xGF(5082305,11,9)!!!!
3*2^5082306+1 is a Factor of xGF(5082305-? ,12,7)!!!!



3*2^5082306+1 is a Factor of GF(5082305-? ,3)!!!! (1215728.376000 seconds)
3*2^5082306+1 is a Factor of GF(5082305,5)!!!! (1215728.391000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,5,3)!!!! (0.000000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305-? ,7,4)!!!! (0.032000 seconds)
3*2^5082306+1 is a Factor of GF(5082305-? ,8)!!!! (0.032000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305-? ,8,3)!!!! (0.032000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,8,5)!!!! (0.047000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,9,5)!!!! (0.000000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305-? ,9,8)!!!! (0.016000 seconds)
3*2^5082306+1 is a Factor of GF(5082305,11)!!!! (0.000000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,11,3)!!!! (0.015000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305-? ,11,5)!!!! (0.000000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,11,8)!!!! (0.016000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305,11,9)!!!! (0.000000 seconds)
3*2^5082306+1 is a Factor of xGF(5082305-? ,12,7)!!!! (0.015000 seconds)

Since Cullen primes are a special form of Proth primes, the Cullen Mega Prime found yesterday might be a (x)(G)FN divisor, am I right? Are we going to test it or would that take too much time?
____________

You are correct, it could be.

Since Cullen primes are a special form of Proth primes, the Cullen Mega Prime found yesterday might be a (x)(G)FN divisor, am I right? Are we going to test it or would that take too much time?

"It appears that the probability of each prime of the form k.2^n+1 dividing a Fermat number is 1/k" (Harvey Dubner & Wilfrid Keller, "Factors of generalized Fermat numbers", Mathematics of Computation, Vol. 64, Number 209, January 1995, pp. 397-405).

Since we're not in a "hurry" with this one, we'll do the "quick" test first and then determine which tests to run afterwards. Yes, it will take longer, but less computing resources will be used.

As you can see from Lennart's "quick" test here:

http://www.primegrid.com/forum_thread.php?id=1291&nowrap=true#14948

although it took almost 2 weeks to test, only the results with the ? would need further testing. It's nice to see confirmation on the 321 prime so we feel comfortable doing it this way for the Cullen.

Once the "quick" test completes, depending on how many ? there are, we may ask again for help.
____________

5_2 done at last after several BOINC-GFN induced crashes...


A GF Factor was found, but the base of 5082274 may not be correct.
3*2^5082306+1 is a Factor of xGF(5082274,5,2)!!!! (425216.233000 seconds)

____________
There are only 10 kinds of people - those who understand binary and those who don't

as I promised:
done some 321llr-workunits with the "slow" phenom for a better benchmark
FFT-Length 327680: 11.25 hours (base: 4 workunits)
FFT-Length 384K: 14.5 hours (base: 7 workunits)
sorry - no more tests at the moment - I had to change the subproject because of the comming challenge ;)

____________
Sysadm@Nbg
my current lucky number: 3749*2^1555697+1
PSA-PRPNet-Stats-URL: http://u-g-f.de/PRPNet/

Hi,

I'm so terribly disappointed ...

These two WUs killed 3 different systems...

pfgw -l10_3.log -gxo10,3 -a2 -q3*2^5082306+1
pfgw -l10_7.log -gxo10,7 -a2 -q3*2^5082306+1

The last killing was 5 Min ago 30000 before finish!

I would like to see, that someone else crunches this two.

If this is possible, take it, otherwise I will crunch them again after the challenge.

Sorry for all that delay because of me

Jörg