Reserved for MF - Sequence 3408

[Dubslow]

Originally Posted by Brownfox

My approximation for cofactors with 90-110 digits is as follows:
Number of factors other than 2 or 3 Expectation (%)

Originally Posted by Dubslow

...So the overall odds of getting a 3^2 is m/(3*2^m), while the overall odds of getting any even power of 3 is m/(2^m*(3 + 27 + 243 + ...)) = 3m/2^(m+3) (since 1/(3+27+243+...) = 3/8).

Using your distribution for m (obviously subject to the same warning about sample size) together with the half-assed theory, I came up with the following theoretical approximation:

In [2]: m_dist = [.014, .028, .138, .244, .235, .157, .088, .060, .023, .009, .005]

In [3]: def odds_of_even_3(m): return 3*m/(2**(m+3))

In [8]: def total_odds_even_3(m_dist):
   ...:     from math import fsum
   ...:     return fsum(odds_of_even_3(m)*odds_m for m, odds_m in enumerate(m_dist, 1))

In [9]: total_odds_even_3(m_dist)
Out[9]: 0.07214776611328125

This compares to

Originally Posted by Brownfox

Chance of getting to an even power of 3 is 0.024

Which is not bad, off by (almost exactly) a factor of 3, and half an order of magnitude is about all I could have hoped for going into it.

[Dubslow]

Actually, now I know for certain that no one read my previous theory post, because it's got some horrifically wrong notation that any middle schooler with algebra should be able to point out.

Specifically, 1/x + 1/y does not equal 1/(x+y).

I'm still pretty sure the final result is "correct" (I was doing the right math in my head, even if what I wrote down is god-awfully wrong), but the last few expressions before that final result are blasphemy before my algebra teachers. So, sorry....

[Brownfox]

All primes to any power. Note that the vast majority are not to a non-unit power.

Regards
Steve

[Dubslow]

Originally Posted by Brownfox

All primes to any power. Note that the vast majority are not to a non-unit power.

Regards
Steve

Hmm, I think that means my number is an underestimate then, since it's overcounting the m for my purposes, and higher m = lower odds.

[RichD]

As a placeholder of work completed, yoyo has finished a full t55 on this number. When interest resurfaces at a later time, I believe only a t60 will be needed before moving to a NFS job.

[swellman]

Originally Posted by RichD

As a placeholder of work completed, yoyo has finished a full t55 on this number. When interest resurfaces at a later time, I believe only a t60 will be needed before moving to a NFS job.

Yoyo@Home just finished up ECM to t60. It is ready for NFS whenever someone is game.

Maybe Ryan will take an interest.

[VBCurtis]

I'll do some poly select this week; this is a small enough job that I can do the CADO select solo.
I'll wait till Tuesday evening or Wed to get started, in case Ryan reserves the job.
If someone else wants to poly select anyway, let me know and I'll post my settings so we don't overlap.

[VBCurtis]

I guess "this week" is 4 months....
Here's a decent poly for this C192:

n: 602838425516071950702800398634448189069057347958670002131123376237344752203259023839151771860497157053376595595747452480360531573609839995416933600183015816569763112349056289178976881268937221
skew: 50211656.838
c0: 6780686882705080323804282112084738299079240200
c1: -615929651998812237047650279903793109285
c2: -8253751695218375720762112293140
c3: 401219187608510740978769
c4: 6364076358300872
c5: -18567360
Y0: -10536642881491562631501019308286051628
Y1: 38473124062368714520009
# MurphyE (Bf=8.590e+09,Bg=4.295e+09,area=1.342e+16) = 1.683e-08

cownoise says skew 65622770.95716 score 1.54501057e-14.
The record for C193 is 1.45e-14, while the record for C192 is very good at 1.80e-14. This number, with leading digit 6, should be about 5% easier than a C193- and this poly is about 7% better than the C193 record.
The search was just over 3 days 20-threaded of CADO search; admax 5M, P=4M, incr=420.
This would be a fairly quick job on 16e if someone would like to test-sieve it; I may do so next month if nobody does it first.

[ryanp]

Originally Posted by VBCurtis

I guess "this week" is 4 months....
Here's a decent poly for this C192

Dank ferrik, has the sequence really been stuck on this c192 for 2+ years now?

Let me take a crack at this blocker. Sieving now...

[VBCurtis]

Thanks, Ryan! We appreciate it.

[ryanp]

Originally Posted by VBCurtis

Thanks, Ryan! We appreciate it.

Sure! Happy to lend a hand.

Looks like I'll be able to form a matrix with ~500M uniques and target_density=120:

Wed Nov 18 11:37:51 2020  commencing full merge
Wed Nov 18 12:06:37 2020  memory use: 7867.1 MB
Wed Nov 18 12:06:47 2020  found 31550239 cycles, need 31145219
Wed Nov 18 12:07:04 2020  weight of 31145219 cycles is about 3737920508 (120.02/cycle)
Wed Nov 18 12:07:04 2020  distribution of cycle lengths:
Wed Nov 18 12:07:04 2020  1 relations: 1469589
Wed Nov 18 12:07:04 2020  2 relations: 2069207
Wed Nov 18 12:07:04 2020  3 relations: 2457009
Wed Nov 18 12:07:04 2020  4 relations: 2541757
Wed Nov 18 12:07:04 2020  5 relations: 2594457
Wed Nov 18 12:07:04 2020  6 relations: 2531814
Wed Nov 18 12:07:04 2020  7 relations: 2440006
Wed Nov 18 12:07:04 2020  8 relations: 2297441
Wed Nov 18 12:07:04 2020  9 relations: 2122314
Wed Nov 18 12:07:04 2020  10+ relations: 10621625
Wed Nov 18 12:07:04 2020  heaviest cycle: 26 relations
Wed Nov 18 12:07:20 2020  commencing cycle optimization
Wed Nov 18 12:08:53 2020  start with 248541919 relations

I have another LA job running on this machine (for A4788 c205) which has ~56 hours to go. In the mean time, I'll sieve a bit more to see if I can form a denser matrix.