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Old 2019-10-23, 10:39   #144
R.D. Silverman
 
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Quote:
Originally Posted by Belteshazzar View Post
<snip>

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(2) Out of date.
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Old 2019-10-23, 15:37   #145
chris2be8
 
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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
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Old 2019-11-18, 20:57   #146
Belteshazzar
 
Feb 2011

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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.
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Old 2020-06-26, 17:10   #147
Belteshazzar
 
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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.
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Old 2020-06-29, 03:18   #148
sean
 
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Quote:
Originally Posted by Belteshazzar View Post
(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.
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Old 2020-06-29, 14:19   #149
Belteshazzar
 
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Quote:
Originally Posted by sean View Post
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.
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