20060408, 15:47  #1  
Sep 2005
Berlin
1000010_{2} Posts 
Factoring humongous Cunningham numbers
Quote:
I found 3793240807030006427627390804715037 as a factor of 4^337  3^337  maybe it is already known. Program output: GMPECM 6.0.1 [powered by GMP 4.1.4] [ECM] Using B1=1000000, B2=839549779, polynomial Dickson(3), sigma=2470101139 Step 1 took 23997ms Step 2 took 9851ms I know, 34 digits are not news these days  but maybe somebody is interested in it. Last fiddled with by axn on 20190808 at 06:24 Reason: Main page URL 

20060408, 16:52  #2 
"William"
May 2003
New Haven
2·3^{2}·131 Posts 
IIRC, Bob Silverman was working a list of a^{n} ± b^{n}.
For numbers close to this form with known interest in the factors, Richard Brent will take factors of a^{337}1, with a < 10,000 and the factors > 10^{9}. At present he lists factors for only a from 2 to 10 and a=337. 
20060408, 23:25  #3  
Nov 2003
3·23·107 Posts 
Quote:
I have done some recent work on extending 3^n +/ 2^n to n = 400. There are about 2 dozen composites left. 

20060410, 14:44  #4  
Nov 2003
3×23×107 Posts 
Quote:
Would anyone like to take a whack at them? 

20060410, 16:01  #5  
"Mark"
Apr 2003
Between here and the
7×11×73 Posts 
Quote:


20060410, 16:47  #6  
Nov 2003
3·23·107 Posts 
Quote:
Here are the remaining composites with n <= 400. 3^n + 2^n 362 (2) 10840121857.C162 367 (1) 6607.13768373.208782631.17491804898039039514781661.C130 371 (1,7,53) 204389653550334425652053.C126 372 (4,12,124) 5953.C111 379 (1) C181 382 (2) 2293.398047057.C170 383 (1) 2756069.C176 386 (2) 5037855841.2420114303415642626173.2923813115488399382449.C131 388 (4) 3881.97777.C175 394 (2) 99289.347671117.182870936735296723148317.C151 400 (16,80) 19995617469086942401.C134 3^n  2^n 335 (1,5,67) 161471.2677857341.459904255060815869460551.C88 337 (1) 9785807.C154 343 (1,7,49) 125539.C136 347 (1) 2083.4855947384634671768060977183621.C132 349 (1) 83757907.51095243093.25596540763065937603.11848591000104763324365120718891.C98 353 (1) 4943.7460934577.3939214450103.7049420316073.C130 359 (1) 719.16208386597057.231558857865697.283082202603561296656613.C118 363 (1,3,11,33,121) 2179.1061406858984187.C87 365 (1,5,73) 944621.C132 367 (1) 2203.3671.17250374783.C158 371 (1,7,53) 743.54167.C141 373 (1) 15667.2262619.249965951.C160 379 (1) 419933.885345041389532803.C158 389 (1) 9337.C182 391 (1,17,23) 4741267.C161 395 (1,5,79) 38711.C144 397 (1) 12509122229.183139575629088302014027581573180839.C145 Note that 3,2,335 and 3,2,363 are totally trivial with SNFS; I just haven't done them. Several others are quite easy. 

20060410, 19:51  #7  
Bamboozled!
May 2003
Down not across
2^{2}×23×107 Posts 
Quote:
If it wasn't that I was too lazy (or, if you prefer the politcally correct excuse, too busy with higher prriority work) I'd do them myself. Should only take a few hours each. Paul 

20060410, 20:16  #8  
Nov 2003
3×23×107 Posts 
Quote:
These numbers are "in the grass" priority.... 

20060410, 21:11  #9 
Nov 2005
48_{10} Posts 
The C87 cofactor of 3^6362^363 factors thusly:
51367404262568392429656240517252067923 x 7705482404964763837578788370404060262063595624219 This factorization was found using Msieve v. 1.01. Last fiddled with by John Renze on 20060410 at 21:15 
20060410, 22:38  #10 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
[SOAPBOX]
John, I would like to thank you for completing this factorization. Sometimes those of us who are committing our resources to more "cutting edge" problems forget that we also need to be grooming new researchers to take our place. Independently solving "simple" problems is both useful for the result and instructive in developing your abilities. Bob Silverman seduced me into participating in a collaborative factoring project decades ago. (At that time a 90MHz Pentium was very much "state of the art"). With his help, I established an automated collaboration to perform widely distributed sieving. NFSNet continues to help push the limits of the Cunningham Project. The "cutting edge" always requires some rather formatible resources. I was unable to perform sufficient filtering on one of our current projects on a machine with 2GB of RAM. But I hope that you have been "bitten" by the bug and will become more active in the NC community. (no, Mike, I don't mean North Carolina) Frankly, we need more new blood. At this point in life, I should ask "Should I wear the bottoms of my trousers rolled?" I'm hoping that my last "hurrah" can be a 1Kb factorization. I hope to see some younger participants ready to step in and fill the places of those who are more suited to "gardening" rather than cuttingedge math. And, to Bob and Paul, we old codgers can still teach the young whipersnappers a thing or two. (Thanks Bob for "infecting" me.) [/SOAPBOX] 
20060410, 23:26  #11 
Nov 2005
2^{4}×3 Posts 
The factors of the C88 are:
1315651155909947565347700897218133001 1338208112877762546551051364373633349610010436196551 
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