20190807, 21:33  #133 
"Ben"
Feb 2007
DFB_{16} Posts 
It's possible the 10^15 figure came from trial division. YAFU (and primesieve) can sieve up to 10^13 in less than an hour; a few hundred hours would get you there, which is a thinkable thought.
Asking yafu to start ECMing the number given an input effort of t50 (use work 50 and v along with the factor function), it will tell you that: Code:
fac: setting target pretesting digits to 209.23 t15: 3777.00 t20: 3777.00 t25: 1510.85 t30: 539.60 t35: 139.90 t40: 31.22 t45: 5.98 t50: 1.02 t55: 0.16 t60: 0.02 
20190923, 16:02  #134 
Feb 2011
2^{5} Posts 
I built a new computer and decided to do some ECM on OEIS wanted numbers as a "burnin test." Ran a couple days' worth of fruitless curves on each of several nearfactorials before successfully factoring Pell(611).
This brings me to two questions: How up to date is the ECM effort listed? It's not shocking that my ECM efforts on nearfactorials didn't come up with anything, but after a week of having my machine do that without success I wondered whether other people had already been down these roads. Also, though the table says factors of Pell(611) are needed for A246556, it's for the 611th term, only 56 terms are listed, and the only bfile is just generated from the entry ergo also only 56 terms. So I don't see where to contribute what I found other than factordb. Last fiddled with by Belteshazzar on 20190923 at 16:03 Reason: too many newlines 
20190923, 18:26  #135  
Sep 2003
5×11×47 Posts 
Quote:
See for instance their sequence of Mersenne prime exponents, which ends at 43112609 because the double checking has only reached approximately 49M so far. 

20190923, 19:45  #136 
Feb 2011
32_{10} Posts 
That's not the issue; all the previous Pell numbers have been fully factored. You can verify this by going to the bfile for the Pell numbers and pasting any of the previous ones into factordb. (I'll admit I haven't queried all of them.)
And Pell(57) is only 22 digits, it's not as though it was some kind of roadblock. So 'what's the smallest primitive factor for each Pell number' didn't encounter some kind of roadblock at 57. 
20190923, 21:18  #137  
Aug 2004
New Zealand
3^{2}×5^{2} Posts 
Quote:
All Pell numbers up to 611 are already factored, hence A246556 is known up to a(610). The OEIS does not always list all known terms of a sequence (and certainly not in the data lines). The first gaps I have are Pell(611), Pell(613), Pell(619), Pell(625). 

20190923, 21:45  #138 
Aug 2004
New Zealand
3^{2}·5^{2} Posts 
I've submitted a bfile for A246556 up to an including a(612).

20190923, 21:55  #139  
Feb 2011
2^{5} Posts 
Quote:
I've gone ahead and submitted the factors of Pell(611) to factordb, and I've made a draft wiki edit reflecting my efforts. I'll try one more thing and then probably give factorization a rest until the next time I have a new machine. 

20190929, 21:07  #140 
Feb 2011
2^{5} Posts 
Pell number 613 has had t50 ecm effort; no factor found. Factored #s 619, 625, and 627.
Then looked at the semiprimes sequence, which is marked 'more,' and found a bunch of small factors. Showed that 859 and 937 belong in the sequence. Ruled out 757, 829, 839, 887, 907. I believe the only candidates remaining <=1000 are 709, 787; both have had t45. I'm done here for a while. 
20190930, 19:57  #141  
Aug 2004
New Zealand
3^{2}·5^{2} Posts 
Quote:


20191023, 07:01  #142 
Feb 2011
100000_{2} Posts 
OK, I lied. I came back to this and did more Pell factorizations. That included all the remaining up to 650 (613 & 631 still unfactored, t50) and some between that and 709. Also a bunch of primeindex ones for the semiprime sequence, finding three and ruling out all the others below 1471 (except 709, 787 as mentioned before); I reported that to oeis. Most of these were very quick.
Also noticed on factordb that (apparently over a year ago) someone did a bunch of primorial+/1 factorizations not noted on the wiki page. For instance, the 1 semiprime sequence contains 503, 709, 859, 863 and the next candidate would be 1013. 
20191023, 07:07  #143  
Feb 2011
2^{5} Posts 
Also, I've never done SNFS before and after your reply
Quote:
So I glanced at your guide to quintic SNFS polys for Fib/Lucas numbers, used pari's lindep to find a couple polys, and tried sieving briefly w/factmsieve and yafu to try to estimate quadcore time for Pell(709) and the 203digit cofactor of Pell(613). As a guess based on this, maybe sieving would take about a month for the latter and two years for the former? Could I get a couple tips here? Here's the polynomial I was looking at: Code:
n: 41992954986653668251498160346091865848259963960853060020750860632150880435788410917184988498688690850646615751221247309950434587076089709352088108916792779996577130820982289749315443146420724344354422429 Y1: 390458526450928779826062879981346977190 Y0: 942650270102046130733437746596776286089 c6: 1 c4: 15 c3: 40 c2: 75 c1: 72 c0: 29 A few questions: 1. One post I saw hinted that the standard advice for skew (c0/cn^1/n) is predicated on Y1=1 or roughly so. What makes sense when Y1 is nowhere close to 1? 2. I see SNFS difficulty computed a couple of different ways. What's the actual general definition? (Including e.g. quadratic second polynomial?) 3. Unless I tell yafu an explicit "size: nnn", here's what it does: Code:
nfs: detected snfs job but no snfs difficulty; assuming size of number is the snfs difficulty nfs: guessing snfs difficulty 271 is roughly equal to gnfs difficulty 30 nfs: creating ggnfs job parameters for input of size 30 4. Given how it did with that, I don't feel I could trust that the parameters it automatically sets when I give it the SNFS difficulty are nearoptimal. I wonder whether its choice of lasieve14 (I'm talking about Pell613 not Pell709 here) is right as well; IIRC factmsieve chooses lasieve15. Downloaded the Silverman "Optimal Parameterization of SNFS" paper, haven't had time to go through it in detail. Hints on params? Last fiddled with by Belteshazzar on 20191023 at 07:09 

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