Brent tables reservations

[sweety439]

Originally Posted by chris2be8

I don't know who found the last 2 factors. Though I suspect they were in http://myfactors.mooo.com/ all along (I forgot to check that since 89^145-1 isn't a first hole).


Now reserving (51^169-1)/(51^13-1) which I've just checked in both factordb and http://myfactors.mooo.com/ (this is the last Brent first hole I can do by SNFS, 43^187-1 is too big for me).

Indeed, when I try to use N-1 proof or N+1 proof for the generalized repunit primes base b (primes of the form (b^n-1)/(b-1)) and the Williams primes base b (primes of the form (b+-1)*b^n+-1 or b^n+-(b+-1), for (b+-1)*b^n+-1 it can be easily use N-1 proof or N+1 proof, since their N-1 or N+1 are trivially 100% factored, while for b^n+-(b+-1) it cannot), and for (b^n-1)/(b-1) or b^n+-(b+-1), either N-1 or N+1 is a product of a small number and a Cunningham number base b (i.e. b^n-1 or b^n+1), and I found many prime factors of the Cunningham numbers b^n+-1 for various bases b which are in factordb but not in http://myfactors.mooo.com/, or in http://myfactors.mooo.com/ but not in factordb (e.g. 202^114+1, in that time, in factordb it is fully factored, while in http://myfactors.mooo.com/ it is not, thus I reported the missing prime factor to http://myfactors.mooo.com/), and thus I reported many prime factors to both factordb and http://myfactors.mooo.com/, even there are such prime factors from 9 digits to 16 digits

(at first, I reported all algebraic factors of b^n+-1 (i.e. b^d+-1 for all d dividing n) to factordb, and I use the "single factorization" of b^n+-1 in http://myfactorcollection.mooo.com:8090/dbio.html, to check the number of the digits of the composites in both factordb and http://myfactors.mooo.com/, and found all missing factors (http://myfactors.mooo.com/ always contain the Aurifeuillian factors, while factordb does not, so I reported all Aurifeuillian factors to factordb, for large bases, the Aurifeuillian factors may not have simple expression)

[chris2be8]

Does anyone know who factored 91^139-1 ? When I checked the last holes after factoring 19^221-1 I noticed it was factored. The factors were not in factordb (just in http://myfactors.mooo.com/) so I added them.

And is anyone working on 91^145-1 ? That had one factor in http://myfactors.mooo.com/ that was not in factordb which made it a c162 (easier than SNFS). If no one else is interested I'll reserve it when I've finished my current work. But knowing how much ECM it has had would be useful (and for other Brent tables entries).

[chris2be8]

No response, so I'll reserve 91^145-1 for ECM, then GNFS if necessary.

[chris2be8]

91^145-1 is done:

Resuming ECM residue saved by chris@4core with GMP-ECM 7.0.5-dev on Wed May 25 02:20:39 2022 
Input number is 226088645816690622526216192237433132289716120596615879258943738679800848841925182810918535350862314783145826431392790171177036695401809764438467711098864889811821 (162 digits)
Using B1=192515022-192515022, B2=35898316301, polynomial Dickson(12), sigma=3:2579256380
Step 1 took 0ms
Step 2 took 12337ms
********** Factor found in step 2: 530977029096293569657298089270576213990222019029061
Found prime factor of 51 digits: 530977029096293569657298089270576213990222019029061
Prime cofactor 425797413875862922863398299445431143067697770734535630010882207961101093249245867331220279940163292093871953161 has 111 digits

[sweety439]

How to use SNFS or GNFS to factor the composite cofactors of 13^282+1 and 13^288+1 (they only have 147 digits and 13^288+1, respectively, also their SNFS difficulty are low)

[BudgieJane]

Originally Posted by sweety439

How to use SNFS or GNFS to factor the composite cofactors of 13^282+1 and 13^288+1 (they only have 147 digits and 13^288+1, respectively, also their SNFS difficulty are low)

I think you meant to say that 13^288+1 only has 152 digits.

[sweety439]

Originally Posted by BudgieJane

I think you meant to say that 13^288+1 only has 152 digits.

Yes, I copy-and-paste, but copied the wrong texts.

So how to use SNFS or GNFS to factor 13^282+1 and 13^288+1? They seems to have low difficulty.

[kruoli]

They have high SNFS difficulty and are better done with GNFS instead.

For GNFS, simply use YAFU(2) or CADO-NFS. It will select everything it needs on it's own.

[swellman]

Originally Posted by sweety439

So how to use SNFS or GNFS to factor 13^282+1 and 13^288+1? They seems to have low difficulty.

YAFU or CADO will give you the necessary polynomials be they SNFS or GNFS, but for an instructive exercise try plugging these expressions into Crombie’s cownoise page (look under Calculators).

The SNFS of each is fairly low (209 and 213 respectively) and a sextic makes for easy sieving.

GNFS is a viable choice as well, though personally I would forgo the GNFS poly search and go right to SNFS.

Give it a try. PM me if you want to discuss further.

[kruoli]

Where is my error thinking that both have >300 SNFS difficulty? Is this wrong because of algebraic factors?

[swellman]

Originally Posted by kruoli

Where is my error thinking that both have >300 SNFS difficulty? Is this wrong because of algebraic factors?

Yes. I do the same thing at times: SNFS = log(13^282+1) = 314 but as you say it ignores the algebraic factors.

Phi() is another tool for generating accurate SNFS polys.