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Forum: Aliquot Sequences 2021-04-13, 16:31
Replies: 1,081
Views: 87,139
Posted By henryzz
Has anyone considered whether SNFS polynomials...

Has anyone considered whether SNFS polynomials exist for s((x*y)^n)?
s(38^100)=36*38^100-2^101-19^101 for example. I can't help thinking there is SNFS polynomial for this but I can't see it.
Forum: Number Theory Discussion Group 2021-04-13, 09:55
Replies: 7
Views: 93
Posted By henryzz
https://en.m.wikipedia.org/wiki/Erd%C5%91s%E2%80%9...

https://en.m.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Kac_theorem#:~:text=The%20Erd%C5%91s%E2%80%93Kac%20theorem%20means,requires%20on%20average%20three%20primes.
The average number of factors is...
Forum: Factoring 2021-04-07, 17:45
Replies: 23
Views: 738
Posted By henryzz
https://sourceforge.net/p/ggnfs/code/441/tree/trun...

https://sourceforge.net/p/ggnfs/code/441/tree/trunk/src/pol5/Readme-ggnfs.txt suggests pol5 also came from ``T. Kleinjung and/or Jens Franke''

This was used alongside msieve cpu polynomial...
Forum: Hardware 2021-04-07, 15:19
Replies: 19
Views: 1,466
Posted By henryzz
Did this test fit in the L3 cache? One or two...

Did this test fit in the L3 cache? One or two workers might fit better. The AVX-512 benchmark could be running into bandwidth issues. More but slower cores is definitely the efficient way to go....
Forum: Prime Gap Searches 2021-04-06, 22:21
Replies: 3
Views: 160
Posted By henryzz
Matt Parker video about prime gaps

I have just watched a youtube video about prime gaps that may be interesting to people here.
SMsTXQYgbiQ
Forum: Prime Gap Searches 2021-04-06, 12:52
Replies: 18
Views: 519
Posted By henryzz
@CraigLo How are you working out your...

@CraigLo How are you working out your probabilities? The obvious calculation is to sum the probabilities for each start point x < 0 that a gap >=xx merit starts there. However, these probabilities...
Forum: Prime Gap Searches 2021-04-06, 12:39
Replies: 18
Views: 519
Posted By henryzz
I think there are a few approaches to this. I...

I think there are a few approaches to this.
I think you are suggesting randomly pick one that matches the res in question, randomize the others and then optimize everything using the previously...
Forum: Hardware 2021-04-06, 12:21
Replies: 19
Views: 1,466
Posted By henryzz
I think it is standard practice for mobile cpus...

I think it is standard practice for mobile cpus to have more execution units as they are less likely to have a discrete gpu.
Forum: Factoring 2021-04-06, 08:40
Replies: 23
Views: 738
Posted By henryzz
Once upon a time GGNFS was a collection of...

Once upon a time GGNFS was a collection of programs that would do a complete factorization itself using the factLat.pl script to pull them together. Many of these tools haven't been used in years for...
Forum: YAFU 2021-04-05, 21:09
Replies: 12
Views: 356
Posted By henryzz
In reality NFS has similar requirements to qs for...

In reality NFS has similar requirements to qs for how many relations are needed. We just count them differently which messes that up. In QS we tend to count full and combined relations while in nfs...
Forum: Prime Gap Searches 2021-04-05, 17:44
Replies: 18
Views: 519
Posted By henryzz
As far as I understand it optimising a range of x...

As far as I understand it optimising a range of x should provide better odds of finding a gap of size y with y < x. We just need to work out the correct ratio of x and y.
Forum: Prime Gap Searches 2021-04-05, 15:25
Replies: 18
Views: 519
Posted By henryzz
220k is nearly a record gap at this size(it was...

220k is nearly a record gap at this size(it was until recently). I would expect a lot of records in 120k-160k range. This size range would be better for maximising record gaps/day rather than the...
Forum: Prime Gap Searches 2021-04-05, 13:22
Replies: 18
Views: 519
Posted By henryzz
That's a nice improvement. How did you find this?...

That's a nice improvement. How did you find this?



I think this shows that it is necessary to pay attention to the target gap size with these searches.
Forum: Prime Gap Searches 2021-04-02, 17:39
Replies: 18
Views: 519
Posted By henryzz
My title is: How do dynamic changes in risk...

My title is: How do dynamic changes in risk factors impact outcomes in patients with atrial fibrillation?
Forum: Prime Gap Searches 2021-04-02, 15:44
Replies: 45
Views: 14,816
Posted By henryzz
We only keep the smallest for each gap size. A...

We only keep the smallest for each gap size. A version of https://primegap-list-project.github.io/lists/prime-gaps-high-watermarks/ that also listed gaps that were second best could be quite fun...
Forum: Prime Gap Searches 2021-04-02, 15:22
Replies: 18
Views: 519
Posted By henryzz
I have discovered that my code for optimizing two...

I have discovered that my code for optimizing two primes at once never ran in that example.

A new solution with a score of 6751 which is a 1.85% reduction:

CRT:...
Forum: Factoring 2021-04-01, 18:00
Replies: 18
Views: 493
Posted By henryzz
Ubuntu would be perfectly fine although if you...

Ubuntu would be perfectly fine although if you have a spare Win 10 licence and that would be more convenient there would be very little downside. I would probably run most stuff under WSL2. The only...
Forum: Prime Gap Searches 2021-04-01, 16:03
Replies: 18
Views: 519
Posted By henryzz
I thought it might be useful for me to share my...

I thought it might be useful for me to share my algorithms for optimizing the offsets for one or two primes. Any improvements or questions would be appreciated.

Algorithm for optimizing one prime...
Forum: Prime Gap Searches 2021-04-01, 15:36
Replies: 18
Views: 519
Posted By henryzz
CRT offsets

In the past using CRT offsets has been considered as an alternative to using a divisor to reduce the density of candidates after sieving. This had some success with small primorials but struggled...
Forum: mersenne.ca 2021-03-31, 21:40
Replies: 597
Sticky: mersenne.ca
Views: 67,036
Posted By henryzz
Yafu has a function that tells it how many txx...

Yafu has a function that tells it how many txx have been run. The number of digits (xx) which provides a value of 1 can be found using https://en.wikipedia.org/wiki/Bisection_method. This is also...
Forum: mersenne.ca 2021-03-30, 13:58
Replies: 597
Sticky: mersenne.ca
Views: 67,036
Posted By henryzz
Binary search with different values?

Binary search with different values?
Forum: Aliquot Sequences 2021-03-30, 07:22
Replies: 9
Views: 320
Posted By henryzz
It's worth noting that if you are running windows...

It's worth noting that if you are running windows 10 then it is possible to run CADO under WSL. Help would be available to set that up.
Forum: Aliquot Sequences 2021-03-27, 21:33
Replies: 20
Views: 485
Posted By henryzz
If you haven't already I would suggest reading...

If you haven't already I would suggest reading https://arxiv.org/abs/1610.07471
Forum: Aliquot Sequences 2021-03-27, 10:08
Replies: 20
Views: 485
Posted By henryzz
The regina_file mentioned above is at...

The regina_file mentioned above is at http://www.aliquotes.com/aliquote_base.htm
Forum: Aliquot Sequences 2021-03-24, 21:24
Replies: 1,081
Views: 87,139
Posted By henryzz
I was thinking that the two programs could be...

I was thinking that the two programs could be combined with that check. With two factors I imagine we could come up with an alternative formula.
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