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Old 2017-05-16, 18:07   #1
BudgieJane
 
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"Jane Sullivan"
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Default 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 2017-05-16 at 18:08
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Old 2017-05-18, 12:41   #2
swellman
 
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What number are you trying to factor?

A recent example is discussed here http://www.mersenneforum.org/showthread.php?t=22317.
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Old 2017-05-18, 18:00   #3
BudgieJane
 
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Quote:
Originally Posted by swellman View Post
What number are you trying to factor?
All numbers a^n ± b^n for 1≤b<a and n>1 and (a,b)=1, going on for ever.

Quote:
Originally Posted by swellman View Post
A recent example is discussed here http://www.mersenneforum.org/showthread.php?t=22317.
Yes, I saw that.

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.
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Old 2017-05-19, 03:04   #4
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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 = 2.260e-011, alpha = -0.092, combined = 1.530e-007, rroots = 0
type: snfs
size: 107
skew: 1.1621
c4: 17
c0: 31
Y1: -14063084452067724991009
Y0: 699053619999045038539170241
m: 6031149606693380230432903286363238884791256368312046189530706734714464935231322816039209826333920537
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Old 2017-05-19, 11:10   #5
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Ideally I'd like to do them up to a,b<1000.
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Old 2017-05-19, 23:54   #6
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I have just spent a very profitable day figuring out what I need to do to specify the polynomials for factoring an ± bn, and I've managed to run a nice 100-digit 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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