Factoring humongous Cunningham numbers

[frmky]

I'm trying out the new save files on those with <506 bits. Here's a hit for 12+5,257:

Input number is 12029311701883957907689034304937942658143192303274525228459040826287469109253891538274048901308766638762299979357 (113 digits)
Using B1=11000000, B2=11000004, sigma=3:803316517-3:803317348 (832 curves)
GPU: Block: 16x32x1 Grid: 26x1x1 (832 parallel curves)
Computing 832 Step 1 took 81212ms of CPU time / 1641781ms of GPU time
Computing 832 Step 2 on CPU took 285ms

Input number is 12029311701883957907689034304937942658143192303274525228459040826287469109253891538274048901308766638762299979357 (113 digits)
Using B1=11000000-11000000, B2=35133391030, polynomial Dickson(12), sigma=3:803317220
Step 1 took 0ms
Step 2 took 13745ms
********** Factor found in step 2: 402984266929957102322279494407189790871178450617
Found prime factor of 48 digits: 402984266929957102322279494407189790871178450617
Prime cofactor 29850574052248989193545685028694637669120007246958199202158529221 has 65 digits

[frmky]

I'll take 7+5,336 for a quick trial SNFS run.

[xilman]

Originally Posted by frmky

Look in the save file to see if X=0x0. If so, it's broken.

X=0x0; CHECKSUM=0; PROGRAM=GMP-ECM 7.0.1-dev; X0=0x0; Y0=0x0;

Bummer.

[unconnected]

4^425-3^425

prp56 = 78781661398887559837662281141443961505557227499537855401
prp62 = 65597237494409113106219655168615127530467247753655240445290751

YAFU correctly detected the special form of number, determined that it is better to use gnfs instead of snfs, but decided to sieve on the -r side with 14e siever. Is this a bug or I'm missing something?

nfs: commencing nfs on c118: 516785935298695014028131273546939635138070898235176891461525586077861157563599026624800
3321976021855073015024440696151
nfs: input divides 4^425 - 3^425
nfs: commencing snfs on c118: 51678593529869501402813127354693963513807089823517689146152558607786115756359902662480
03321976021855073015024440696151
nfs: input snfs form is better done by gnfs: difficulty = 204.70, size = 144
nfs: commencing poly selection with 8 threads
nfs: setting deadline of 1406 seconds
nfs: completed 212 ranges of size 250 in 1478.3857 seconds
nfs: best poly = # norm 3.209350e-11 alpha -7.091678 e 3.745e-10 rroots 5

[bsquared]

Probably a bug. Likely it didn't go back to evaluate sides after having already done so when finding the snfs poly. You can restart with -a on the command line to use algebraic side.

[frmky]

Since Paul's site is still down, I've factored these so far. I'm putting all my results in factordb.com.

5-2,441
7+5,357
7+5,363
7+6,336
8-3,309
9-2,315
10+9,306
12+11,285
12-11,285

[xilman]

Originally Posted by frmky

Since Paul's site is still down, I've factored these so far. I'm putting all my results in factordb.com.

5-2,441
7+5,357
7+5,363
7+6,336
8-3,309
9-2,315
10+9,306
12+11,285
12-11,285

Oh dear. Down again?

It seems to be back now, so I'll add recent results and update the page.

BTW, I received all these by email, my preferred means of communication. Greg knows this so think of it as a gentle reminder to others. However, Greg's post also serves notice to others who may otherwise be tempted to waste time on these candidates, so please feel free to post here as well as emailing me.

Paul

[xilman]

Originally Posted by jyb

Thanks for the update, Paul. Here are some additions and corrections:

1) The sieving for 4-3,409 and 6+5,316 (shown above) was done by NFS@Home, with post-processing by Rich Dickerson. I don't know if you want the credit to reflect that.

2) You may want to have Serge verify his factoring method. The factors for 11+8,289, 5-4,397, and 6+5,383 (shown above) were almost certainly found by ECM.

3) 5-2,353 was factored by Greg Childers and NFS@Home, finishing on 2016-03-30. This date is before your April 1 cutoff, so I don't know how you want to handle that.

4) 6+5,317 was factored by Rich Dickerson and NFS@Home, reported on 2016-03-31. This one is already reflected in your tables, but doesn't appear in either the UPDATE.txt or HISTORICAL.txt files. Same issue with the April 1 cutoff.

1) Now added credit.

2) Corrected.

3) Decided it will go into UPDATE.txt because I didn't learn about it until April 7.

4) Ditto.

Thanks for the proof reading. Things can get a little hectic when factors come flooding in and errors are made.

Paul

[xilman]

Originally Posted by xilman

It seems to be back now, so I'll add recent results and update the page.

Now updated. Please let me know of any errors.

Paul

[unconnected]

4^451+3^451

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2714632188
Step 1 took 116721ms
Step 2 took 35901ms
********** Factor found in step 2: 7223419090702674950895250983822046673260009
Found probable prime factor of 43 digits: 7223419090702674950895250983822046673260009
Probable prime cofactor <...> has 152 digits

[unconnected]

4^443+3^443

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2684575918
Step 1 took 113518ms
Step 2 took 36152ms
********** Factor found in step 2: 26547165838734827895448382886534887411467
Found probable prime factor of 41 digits: 26547165838734827895448382886534887411467
Probable prime cofactor <...> has 187 digits