10+7,306:
[code]
134338551910206099464711322988037556605709829879974332790130506577
3345718031639807230979034064130243221119610215568890655113117565473355484295811378114690921
[/code]

[QUOTE=EdH;527736]10+7,306:
[code]
134338551910206099464711322988037556605709829879974332790130506577
3345718031639807230979034064130243221119610215568890655113117565473355484295811378114690921
[/code][/QUOTE]

Thanks, Ed. Can you please indicate in these posts what factoring method you employed? Your numbers are close to the edge between using SNFS and GNFS. (Though your current reservation is a clear SNFS job.)

[QUOTE=jyb;527743]Thanks, Ed. Can you please indicate in these posts what factoring method you employed? Your numbers are close to the edge between using SNFS and GNFS. (Though your current reservation is a clear SNFS job.)[/QUOTE]
Sure Jon. Since you pointed me toward SNFS and I've had some success, all the latest have been SNFS:
[code]
10+3,259
8-3,287
10+7,306
[/code]And, I'm focusing there for now, trying to get some more experience (although my script is running well enough that I'm probably not learning what I could by hand).
-Ed

FWIW I did a little testing and found the following to best sieved by GNFS:
[CODE]8+5,327
7-5,305
10+3,260
[/CODE]

YMMV. I’m still working through the C14X GNFS jobs but of course the above HCNs are unreserved.

12+5,276 (SNFS):
[code]
5898094500415161901226156546184395788593394887430441502117224328355142537
223789392305558893703950398250332783951617297246469235418372827066300383396864967921
[/code]

[QUOTE=swellman;527802]FWIW I did a little testing and found the following to best sieved by GNFS:
[CODE]8+5,327
7-5,305
10+3,260
[/CODE]

YMMV. I’m still working through the C14X GNFS jobs but of course the above HCNs are unreserved.[/QUOTE]

Can you tell me how you determined this? You are certainly correct for the latter two, since those have to be quartics. But I am very surprised to hear that 8+5,327 sieves better as GNFS. Are you sure you tested it as a sextic for SNFS, or did you use a quartic?

8+5_321 was factored:


[CODE]p66 factor: 211677698715772406313538601890873669956681228665256392252152683169
p112 factor: 2148278550952695182813710780007275166485413406325586160675942816742330193451449541013111481893641146139122217651[/CODE]
This was factored with SNFS with a combination of CADO-NFS for sieving and msieve for post-processing. The post-processing of CADO failed in square root for some reason (and was not resolved by switching to the newest version or changing the number of characters). msieve was fine after sieving some more relations (see attached log file).

[QUOTE=jyb;527818]Can you tell me how you determined this? You are certainly correct for the latter two, since those have to be quartics. But I am very surprised to hear that 8+5,327 sieves better as GNFS. Are you sure you tested it as a sextic for SNFS, or did you use a quartic?[/QUOTE]

Yafu determination. Not authoritative I realize but it means 8+5_327 is right on the line between the two methods. Dealer’s choice I suppose.

The two quartics are far less efficient than GNFS as you point out.

[QUOTE=swellman;527823]Yafu determination. Not authoritative I realize but it means 8+5_327 is right on the line between the two methods. Dealer’s choice I suppose.

The two quartics are far less efficient than GNFS as you point out.[/QUOTE]

Do you know how yafu checks it? Does it try both quartic and sextic? And does it have to find a polynomial in order to check GNFS? If it does the latter, then it has already put work into GNFS, which might explain why that could be subsequently easier.

[QUOTE=jyb;527825]Do you know how yafu checks it? Does it try both quartic and sextic? And does it have to find a polynomial in order to check GNFS? If it does the latter, then it has already put work into GNFS, which might explain why that could be subsequently easier.[/QUOTE]
I can't speak to how YAFU does its checking, but it does choose between different sizes and whether to run algebraic or rational. It does all this immediately, so there can't be much, if any, sieving.

Note this run for 8-5,333 with time stamps:
[code]
$ date;./yafu "snfs(8^333-5^333,336461381514797276207642148518108475050843422073756451845341352195243062509128375963395098967621873394398186280542937539984275327774268348941333924744177100747)" -v -np;date
Sat Oct 12 14:27:50 EDT 2019

10/12/19 14:27:50 v1.35-beta @ localhost.localdomain, System/Build Info:
Using GMP-ECM 7.0.3, Powered by GMP 6.1.1
detected Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz
detected L1 = 32768 bytes, L2 = 4194304 bytes, CL = 64 bytes
measured cpu frequency ~= 2394.041760
using 1 random witnesses for Rabin-Miller PRP checks

===============================================================
======= Welcome to YAFU (Yet Another Factoring Utility) =======
======= [EMAIL="bbuhrow@gmail.com"]bbuhrow@gmail.com[/EMAIL] =======
======= Type help at any time, or quit to quit =======
===============================================================
cached 78498 primes. pmax = 999983

>> nfs: checking for job file - job file found, testing for matching input
nfs: number in job file does not match input
nfs: checking for poly file - no poly file found
nfs: commencing nfs on c301: 5357543035931336604742125245300009052807024058527668037218751941851698106255116498716881104901064023590000769088024594192874970136300188586196951877565515000874275285929656339992868601119574543870862895138966935377120468571601108078713967709988108665300450637534989699538838390173717329050164113331563
nfs: searching for brent special forms...
nfs: searching for homogeneous cunningham special forms...
nfs: input divides 8^333 - 5^333
nfs: degree 4 difficulty = 200.49, degree 6 difficulty = 200.49
nfs: choosing degree 6
nfs: guessing snfs difficulty 200 is roughly equal to gnfs difficulty 142
nfs: creating ggnfs job parameters for input of size 142

gen: ========================================================
gen: selected polynomial:
gen: ========================================================

n: 336461381514797276207642148518108475050843422073756451845341352195243062509128375963395098967621873394398186280542937539984275327774268348941333924744177100747
# 8^333-5^333, difficulty: 200.49, anorm: 3.00e+36, rnorm: 2.60e+39
# scaled difficulty: 200.49, suggest sieving algebraic side
# size = 6.442e-10, alpha = 1.996, combined = 1.236e-11, rroots = 0
type: snfs
size: 200
skew: 1.0000
c6: 1
c3: 1
c0: 1
Y1: -72759576141834259033203125
Y0: 2596148429267413814265248164610048
m: 143022531024129027886422073040388330584920273476147055817627363119887057129669877176260812805793416638218711847875140034803782143559700662243887572598710337267
nfs: job file is missing params, filling them

***factors found***

***co-factor***
C159 = 336461381514797276207642148518108475050843422073756451845341352195243062509128375963395098967621873394398186280542937539984275327774268348941333924744177100747

ans = 336461381514797276207642148518108475050843422073756451845341352195243062509128375963395098967621873394398186280542937539984275327774268348941333924744177100747

Sat Oct 12 14:27:50 EDT 2019
[/code]It shows less than a second.

B^2 is the expert on Yafu, but I believe it tries to find a SNFS fit, picks the best one (through test sieving on higher difficulty levels than Ed’s example above) and goes with that. If there is no SNFS form found it defaults to GNFS. If GNFS is lower than the SNFS equivalent, it goes with GNFS (this step sometimes occurs early in the process).

In no case does Yafu attempt to generate a GNFS poly. Yafu just looks at SNFS vs GNFS difficulties and picks accordingly.

B^2 posted [url=https://www.mersenneforum.org/showpost.php?p=527082&postcount=396]an example[/url] of SNFS generation recently, with further discussion in that thread.