mersenneforum.org Numbers wanted for OEIS sequences
 Register FAQ Search Today's Posts Mark Forums Read

2019-10-23, 10:39   #144
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by Belteshazzar Downloaded the Silverman "Optimal Parameterization of SNFS" paper, haven't had time to go through it in detail. Hints on params?

Parameters suggested therein are:

(1) Based on a line siever
(2) Out of date.

 2019-10-23, 15:37 #145 chris2be8     Sep 2009 1000100101102 Posts I'd use parms as suggested below. That's a cut down version of factMsieve.pl which just sanity checks the poly and reports varios stats about it. The most useful is the msieve rating which includes the e-score. Which is about right for SNFS 234. Code: \$ rate_poly.pl t.poly -> __________________________________________________________ -> | This is the factMsieve.tester.pl script for GGNFS. | -> | This program is copyright 2004, Chris Monico, and subject| -> | to the terms of the GNU General Public License version 2.| -> |__________________________________________________________| This is the tester script, it just checks the poly without sieving any relations -> Starting Wed Oct 23 16:26:56 2019 -> Working with NAME=t... -> Selected default factorization parameters for degree 6 snfs 234.190 digit level. -> Selected lattice siever: /home/chris/lasieve4_64/gnfs-lasieve4I15e SNFS DIFF is about 234.190, GNFS equiv is about 168.6168, GNFS DIFF is about 202.623, degree 6. -> Using rlim=56000000, alim=56000000, lpbr=30, lpba=30, mfbr=60, mfba=60, rlambda=2.6, alambda=2.6, qintsize 100000 -> Using calculated skew 1.75280256323576 aa is 32768, bb is 16384, degree is 6, c6 is 1, c0 is 29, Y1 is 390458526450928779826062879981346977190, Y0 is -942650270102046130733437746596776286089 sqr_lim is 7483.31477354788, sqrt(skew) is 1.32393450111241, aa is now 324646293.057838, bb is now 92607775.646598 c0 is 29, adding 1.8292906548684e+49 c1 is -72, adding -1.59213617317567e+50 c2 is 75, adding 5.81395909450559e+50 c3 is -40, adding -1.08701038969571e+51 c4 is 15, adding 1.4289859479919e+51 c6 is 1, adding 1.17074601911578e+51 -> Algebraic norm is 1.95319677609365e+51. Rational norm is 2.14057657931935e+47. -> Algebraic difficulty is about 51.2907. Rational difficulty is about 47.3305. msieve rating: skew 1.75, size 1.055e-11, alpha 1.681, combined = 6.609e-13 rroots = 0 It's probably OK Chris
 2019-11-18, 20:57 #146 Belteshazzar   Feb 2011 25 Posts Finally got Pell(613) though the parameters I used (yafu default) turned out to be far from optimal, see this other thread. The next remaining are 631 and 653. 631, the two semiprime roadblocks 709 and 787, and many of the other nearby remaining numbers can all use the same algebraic polynomial. So I wonder whether, if someone were to ever try to do 787 (301 digits), it might make sense for them to do something like the 'factorization factory' approach and knock out a bunch of the others too.
 2020-06-26, 17:10 #147 Belteshazzar   Feb 2011 25 Posts I factored several numerators of harmonic numbers for the sequence of their semiprimes http://oeis.org/A153357 . (This calls them Wolstenholme numbers but that appears to contradict standard terminology & should be fixed.) Numerator(H_371)=p49+p112 is in Numerator(H_377)=p33+p58+p71 is ruled out Numerator(H_391)=c169 has had t52 ECM (7550@43e6+5000@11e7), ready for NFS Numerator(H_421)=p33+p151 is in Numerator(H_436)=p49+p138 is in Numerator(H_472)=p40+c168 ruled out Numerator(H_476)=c207 has had t51 ECM Numerator(H_480)=p43+p168 is in It appears that 385, 414, 425, 451, 452 were already shown to be in the sequence years ago and these are all the candidates below 500.
2020-06-29, 03:18   #148
sean

Aug 2004
New Zealand

32×52 Posts

Quote:
 Originally Posted by Belteshazzar (This calls them Wolstenholme numbers but that appears to contradict standard terminology & should be fixed.)
I'm not sure what you mean by this. All the places I checked refer to these as the
Wolstenholme numbers.

2020-06-29, 14:19   #149
Belteshazzar

Feb 2011

25 Posts

Quote:
 Originally Posted by sean I'm not sure what you mean by this. All the places I checked refer to these as the Wolstenholme numbers.
Standard terminology is to refer to the numerators of the sums of 1/n^2, i.e. the generalized harmonic numbers H_{n,2}, as Wolstenholme numbers, not the numerators of the normal harmonic numbers. If you look at the bottom of A001008, to which A153357 refers, you find this comment:
Quote:
 Changed title, deleting the incorrect name 'Wolstenholme numbers' which conflicted with the definition of the latter in both Weisstein's World of Mathematics and in Wikipedia, as well as with OEIS A007406. - Stanislav Sykora, Mar 25 2016
Hisanori Mishima's 'World Integer Factorization Center,' which had kept records for these and is linked from A153357, is probably the source of the confusion. He refers to numerators of any generalized harmonic numbers as Wolstenholme numbers, and uses the notation Wrn=Numerator(H_{n,r}). But Wolstenholme's theorem only deals with the numerators of harmonic numbers H_{p-1,1} and of H_{p-1,2}, not with all r.

 Similar Threads Thread Thread Starter Forum Replies Last Post ChristianB Aliquot Sequences 16 2014-05-16 06:56 kosta Factoring 24 2013-03-21 07:17 Raman Other Mathematical Topics 20 2012-08-22 16:05 Greebley Aliquot Sequences 6 2012-04-07 10:06 science_man_88 Miscellaneous Math 11 2011-05-18 15:04

All times are UTC. The time now is 20:49.

Sat Dec 4 20:49:31 UTC 2021 up 134 days, 15:18, 1 user, load averages: 1.35, 1.26, 1.25