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Search took 0.03 seconds. Search: Posts Made By: charybdis
Forum: Forum Feedback 2021-03-02, 14:46
Replies: 15
Views: 329
Posted By charybdis
Several people have already shed light on what's...

Several people have already shed light on what's happening. When we run LL with a shift, we are not just starting with a different power of 2 and iterating x^2-2. We're also shifting the 2 that we...
Forum: Forum Feedback 2021-03-02, 01:48
Replies: 15
Views: 329
Posted By charybdis
The 2 that's subtracted at each iteration needs...

The 2 that's subtracted at each iteration needs to be bit-shifted too. This ensures that the residue at each iteration is just a shifted version of the "correct" residue, but the squarings that are...
Forum: Cunningham Tables 2021-02-28, 13:51
Replies: 17
Views: 1,619
Posted By charybdis
Pleased to see that Sam has credited me with a...

Pleased to see that Sam has credited me with a new record ECM factor :razz:

3458 2,2750M c185 33064259907061907187454540598801861343151128939115124241607813225512323356759645078501. p99 Balfour...
Forum: Cunningham Tables 2021-02-27, 18:41
Replies: 17
Views: 1,619
Posted By charybdis
That sounds like a good plan to start out with;...

That sounds like a good plan to start out with; in the long term maybe it would be best to move on to 850e6 after the first 19000@260e6, given that Yoyo won't be the only ones running ECM on these...
Forum: Cunningham Tables 2021-02-26, 19:25
Replies: 17
Views: 1,619
Posted By charybdis
2,2786M c219 = p56 * c163 (GNFS in progress)

Can confirm that ECM is very much worthwhile:

Input number is...
Forum: Aliquot Sequences 2021-02-23, 17:23
Replies: 28
Views: 900
Posted By charybdis
The Murphy-E scores from msieve and CADO aren't...

The Murphy-E scores from msieve and CADO aren't directly comparable - in fact this has a slightly worse score than the msieve poly (5.584e-12 according to cownoise.com). But that's not surprising...
Forum: Aliquot Sequences 2021-02-22, 17:46
Replies: 28
Views: 900
Posted By charybdis
Happy to help out if/when the numbers get a bit...

Happy to help out if/when the numbers get a bit bigger, but I wouldn't want to ruin the fun so I'll stay away for now.
Forum: Miscellaneous Math 2021-02-19, 13:01
Replies: 32
Views: 1,377
Posted By charybdis
Say N = kM with k being the known factors and M...

Say N = kM with k being the known factors and M the unfactored part. Find a such that y := a^2 mod M is around sqrt(M). We want x such that x^2 = y mod N, so we also need x^2 = y mod p for each prime...
Forum: Cunningham Tables 2021-02-19, 03:02
Replies: 236
Views: 47,435
Posted By charybdis
OK, might as well send them myself then...

OK, might as well send them myself then...
Forum: Cunningham Tables 2021-02-19, 02:26
Replies: 236
Views: 47,435
Posted By charybdis
Good job everyone! 20 days from start to finish...

Good job everyone! 20 days from start to finish isn't too shabby :smile:

Curtis, have you sent the factors to Sam Wagstaff?
Forum: Cunningham Tables 2021-02-19, 01:42
Replies: 236
Views: 47,435
Posted By charybdis
It's been a few weeks. Guessing you put this on...

It's been a few weeks. Guessing you put this on hold to work on something else?
Forum: Miscellaneous Math 2021-02-19, 01:31
Replies: 32
Views: 1,377
Posted By charybdis
Well yes, it does help that we already know 6...

Well yes, it does help that we already know 6 factors of F12 :smile:
Forum: Miscellaneous Math 2021-02-17, 18:24
Replies: 32
Views: 1,377
Posted By charybdis
Negative values are fine because we can include...

Negative values are fine because we can include -1 in the factor base. In this case we get (m*2^4096)^2 = m^2*(2^8192+1) - m^2, so this reduces to -m^2.



Indeed. But by "small", I meant "around...
Forum: Miscellaneous Math 2021-02-17, 16:47
Replies: 32
Views: 1,377
Posted By charybdis
For p = 2^8192+1, yes: just set x = m*2^4096. But...

For p = 2^8192+1, yes: just set x = m*2^4096. But those trivial examples end up providing the trivial factorization. Here's a non-trivial example:
x =...
Forum: Miscellaneous Math 2021-02-17, 15:20
Replies: 32
Views: 1,377
Posted By charybdis
As I said: Finding x such that x^2 mod...

As I said:



Finding x such that x^2 mod N is small is NOT the bit that becomes difficult for very large numbers. So unless you demonstrate an efficient way of finding x for which x^2 mod N is...
Forum: Miscellaneous Math 2021-02-17, 14:09
Replies: 32
Views: 1,377
Posted By charybdis
Right, if N is the number we want to factor, we...

Right, if N is the number we want to factor, we can find these very quickly by looking for values of k where sqrt(kN) is close to an integer.

But the problem isn't finding values of x where x^2...
Forum: YAFU 2021-02-16, 18:08
Replies: 4
Views: 455
Posted By charybdis
These are a bit small, especially anorm; the code...

These are a bit small, especially anorm; the code uses a = 1e6*sqrt(skew), b=1e6/sqrt(skew) which might work well for small jobs but for numbers this large 1e6 is a big underestimate.

Really it...
Forum: Cunningham Tables 2021-02-12, 22:25
Replies: 17
Views: 1,619
Posted By charybdis
Does not imply that the extension won't be...

Does

not imply that the extension won't be merged into the main tables until most of the easy sextics are done? Or does that line only apply to ECM efforts?
Forum: Msieve 2021-02-11, 00:46
Replies: 179
Views: 37,605
Posted By charybdis
c185

2,2750M

n: 31647571313134323652609296402268897329689252390097206333060347128266343802277166957713755129362162253418129502007399985053315681820678031516478144277440761942221352978166693923227077001...
Forum: Factoring 2021-02-08, 12:22
Replies: 1,816
Views: 148,565
Posted By charybdis
Ah yes, of course. In fact it's the same...

Ah yes, of course. In fact it's the same algebraic poly for 3+2_1494L.

There's also 3+2_1566L at difficulty 250.
Forum: Factoring 2021-02-07, 14:10
Replies: 1,816
Views: 148,565
Posted By charybdis
Aren't there three easy sextics in the 230s, or...

Aren't there three easy sextics in the 230s, or am I mistaken?

8+3_774L
x^6-144*x^4-288*x^3+5184*x^2+20736*x+13824
96479729228174488169059713024*x-680564733841876927255006182258073500539 =...
Forum: Cunningham Tables 2021-02-07, 12:55
Replies: 17
Views: 1,619
Posted By charybdis
...though those divisible by 9 still have...

...though those divisible by 9 still have sextics.

For the non-Aurifeuillians, the exponents divisible by 17 are probably fastest with an octic that makes use of the algebraic factor.
Forum: Cunningham Tables 2021-01-30, 19:14
Replies: 17
Views: 1,619
Posted By charybdis
Taking 2,1431+ c184 and 2,2750M c185.

Taking 2,1431+ c184 and 2,2750M c185.
Forum: Cunningham Tables 2021-01-20, 13:12
Replies: 236
Views: 47,435
Posted By charybdis
That looks a lot more than 30M relations short to...

That looks a lot more than 30M relations short to me. To get a good matrix I'd want the initial number of relations to be a bit bigger than the number of ideals, so you probably want 100M more raw...
Forum: Factoring 2021-01-19, 15:47
Replies: 933
Views: 82,363
Posted By charybdis
grep -v ",[8-9a-f]........$" should remove all...

grep -v ",[8-9a-f]........$" should remove all lines ending with a 36-bit prime, which is what we need.
Showing results 1 to 25 of 192
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