20170516, 18:07  #1 
"Jane Sullivan"
Jan 2011
Beckenham, UK
352_{8} Posts 
snfs for homogeneous cunninghams with a,b>12
Pardon my ignorance, but how can I persuade YAFU to run snfs on homogeneous Cunningham numbers where a and b can take any values (including >12) subject to the usual constraints? I assume this will require me to input my own polynomial, etc.
Last fiddled with by BudgieJane on 20170516 at 18:08 
20170518, 12:41  #2 
Jun 2012
2×5×7×41 Posts 
What number are you trying to factor?
A recent example is discussed here http://www.mersenneforum.org/showthread.php?t=22317. 
20170518, 18:00  #3  
"Jane Sullivan"
Jan 2011
Beckenham, UK
2×3^{2}×13 Posts 
All numbers a^n ± b^n for 1≤b<a and n>1 and (a,b)=1, going on for ever.
Quote:
What would be really nice is if snfs allowed "Homoeneous Cunninghams" to include values of a and b above 12, even though I have been reminded that those additional numbers are not really homogeneous Cunninghams. 

20170519, 03:04  #4 
"Ben"
Feb 2007
110011011111_{2} Posts 
The development version of yafu will find them up to a,b < 51.
Code:
nfs: commencing nfs on c101: 15067758128205500531528890729654007316625403247110194481701428976958933222260247689424312462463918293 nfs: searching for brent special forms... nfs: searching for homogeneous cunningham special forms... nfs: input divides 31^71 + 17^71 . . . gen: ======================================================== gen: selected polynomial: gen: ======================================================== n: 15067758128205500531528890729654007316625403247110194481701428976958933222260247689424312462463918293 # 31^71+17^71, difficulty: 107.38, anorm: 4.59e+025, rnorm: 6.48e+032 # scaled difficulty: 108.57, suggest sieving rational side # size = 2.260e011, alpha = 0.092, combined = 1.530e007, rroots = 0 type: snfs size: 107 skew: 1.1621 c4: 17 c0: 31 Y1: 14063084452067724991009 Y0: 699053619999045038539170241 m: 6031149606693380230432903286363238884791256368312046189530706734714464935231322816039209826333920537 
20170519, 11:10  #5 
"Jane Sullivan"
Jan 2011
Beckenham, UK
EA_{16} Posts 
Ideally I'd like to do them up to a,b<1000.

20170519, 23:54  #6 
"Jane Sullivan"
Jan 2011
Beckenham, UK
2×3^{2}×13 Posts 
I have just spent a very profitable day figuring out what I need to do to specify the polynomials for factoring a^{n} ± b^{n}, and I've managed to run a nice 100digit example to prove that it works.
I'd like to thank those who have written various messages not just in this thread, but in several others (including "SNFS Polynomial selection help"). 
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