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Search: Posts Made By: charybdis
Forum: Miscellaneous Math 2021-04-22, 22:45
Replies: 21
Views: 401
Posted By charybdis
Once they've passed once, of course they'll...

Once they've passed once, of course they'll "always pass". Running the same thing over and over isn't going to give you different results.

So maybe your test actually is good, or maybe you just...
Forum: Miscellaneous Math 2021-04-22, 21:50
Replies: 21
Views: 401
Posted By charybdis
I believe that the methods used to search up to...

I believe that the methods used to search up to such large bounds rely on the same set of bases being used for every n, which is not the case for your test. Someone with more knowledge in this area...
Forum: Homework Help 2021-04-22, 17:04
Replies: 2
Views: 46
Posted By charybdis
(Assuming you mean the axioms from the book you...

(Assuming you mean the axioms from the book you gave in your other thread)
Hint: use the cancellation law.

Suppose ab = 0 and b =/= 0. The book gives a proof that anything multiplied by 0 is 0,...
Forum: CADO-NFS 2021-04-22, 14:32
Replies: 490
Sticky: CADO NFS
Views: 75,771
Posted By charybdis
This would be useful if, say, your machine has 16...

This would be useful if, say, your machine has 16 threads and you only want to use 8 of them for CADO. But then you could use -t 8 and I'm not sure what the difference is.



If you want to use...
Forum: Homework Help 2021-04-22, 14:05
Replies: 31
Views: 1,258
Posted By charybdis
That's about the least clear you could possibly...

That's about the least clear you could possibly have made it. It's unlikely that your computer won't run the ggnfs sievers: the assembly code hasn't been updated since the core-2 era, so they ought...
Forum: Miscellaneous Math 2021-04-22, 12:45
Replies: 21
Views: 401
Posted By charybdis
What makes you believe that your test is better...

What makes you believe that your test is better than doing Miller-Rabin to the first 5 or 7 primes, or indeed any set of randomly chosen bases? As far as I can see there is no numerical or...
Forum: Homework Help 2021-04-21, 22:35
Replies: 31
Views: 1,258
Posted By charybdis
If you're having problems setting up ggnfs, post...

If you're having problems setting up ggnfs, post in the Factoring subforum, making it clear exactly what the issues are, and there will be plenty of people willing to help you. It's almost certainly...
Forum: Homework Help 2021-04-21, 12:29
Replies: 31
Views: 1,258
Posted By charybdis
"Homework help" does not mean "get others to do...

"Homework help" does not mean "get others to do all your work for you". I already gave you some advice earlier in the thread:
Forum: Miscellaneous Math 2021-04-19, 20:43
Replies: 26
Views: 549
Posted By charybdis
This test calculates [$]3^{\left\lfloor...

This test calculates [$]3^{\left\lfloor \frac{2^p-1}{p}\right\rfloor} \pmod {2^p-1}[/$]. Fermat's little theorem tells us that p divides 2^p-2, so we are in fact calculating [$]3^{\frac{2^p-2}{p}}...
Forum: Miscellaneous Math 2021-04-19, 12:23
Replies: 26
Views: 549
Posted By charybdis
You can verify this by going to the link below: ...

You can verify this by going to the link below:

https://pari.math.u-bordeaux.fr/dochtml/html-stable/

Clicking on Q in the lower left
And then clicking on qfbprimeform on top.[/QUOTE]

If you...
Forum: Miscellaneous Math 2021-04-18, 13:14
Replies: 26
Views: 549
Posted By charybdis
:no: The discussion in this thread is about...

:no:

The discussion in this thread is about when 9 is a quadratic residue mod n, not when n is a quadratic residue mod 9.

OP, you seem to have assumed we can use Euler's criterion to check...
Forum: Factoring 2021-04-15, 13:46
Replies: 7
Views: 331
Posted By charybdis
1/3 might be slightly higher than optimal,...

1/3 might be slightly higher than optimal, although what's best will depend on what software you're using for GNFS. I've used 0.32 when running ggnfs via YAFU (factmsieve.py would be similar), and...
Forum: NFS@Home 2021-04-14, 16:25
Replies: 124
Views: 12,552
Posted By charybdis
It scores the same because, to all intents and...

It scores the same because, to all intents and purposes, it is the same. If the algebraic poly is f (degree d) and the rational poly is g, then a relation is given by a pair (a,b) for which the...
Forum: NFS@Home 2021-04-14, 14:36
Replies: 124
Views: 12,552
Posted By charybdis
Sure, but not for any mathematical reason. If we...

Sure, but not for any mathematical reason. If we flip the sign of Y0 or Y1, then we flip the sign of the root, so if we also flip the signs of the odd-degree coefficients of the algebraic poly then...
Forum: NFS@Home 2021-04-14, 12:31
Replies: 124
Views: 12,552
Posted By charybdis
-17^34 is a root of both polys so this is fine.

-17^34 is a root of both polys so this is fine.
Forum: Data 2021-04-14, 03:00
Replies: 17
Views: 555
Posted By charybdis
P-1 is particularly useful for GIMPS because we...

P-1 is particularly useful for GIMPS because we can take advantage of the fact that all factors of 2^p-1 are of the form 2kp+1: we only need k to be smooth wrt B1/B2 in order to find the factor. P+1...
Forum: Number Theory Discussion Group 2021-04-13, 12:50
Replies: 7
Views: 126
Posted By charybdis
Indeed, and it's trivial to construct a...

Indeed, and it's trivial to construct a counterexample. But they are the same for ω(n), and in fact to prove the result I gave above one would want to deal with [$]\sum_{n\leq x}\omega(n)[/$] first,...
Forum: Number Theory Discussion Group 2021-04-13, 11:19
Replies: 7
Views: 126
Posted By charybdis
A fun exercise is to deduce from Mertens' theorem...

A fun exercise is to deduce from Mertens' theorem
[$$]\sum_{p\leq x}\frac{1}{p} = \log\log x + M + o(1)[/$$]
(where M is a constant) that
[$$]\sum_{n\leq x}|\omega(n)-\log\log n|^2 = O(x\log\log...
Forum: Aliquot Sequences 2021-04-11, 17:40
Replies: 2,957
Views: 209,038
Posted By charybdis
The c191 at line 12590 has survived ~half a t60...

The c191 at line 12590 has survived ~half a t60 so far and will soon be ready for GNFS; it's probably OK for the usual suspects to start poly selection now.

I suppose this is near the crossover...
Forum: YAFU 2021-04-11, 16:51
Replies: 37
Views: 1,090
Posted By charybdis
Looks good now. Thank you!

Looks good now. Thank you!
Forum: YAFU 2021-04-10, 12:58
Replies: 2
Views: 111
Posted By charybdis
The -B1ecm option only affects ecm(), not...

The -B1ecm option only affects ecm(), not factor().

You can use -work to specify how much ECM has already been run on a number: -work 30 would mean that ECM is already complete to the 30-digit...
Forum: YAFU 2021-04-10, 12:50
Replies: 12
Views: 411
Posted By charybdis
Each dependency is a single solution to the...

Each dependency is a single solution to the equations, i.e. a set of columns of the matrix which add to 0. At the end of the linear algebra you'll see something like "recovered 30 nontrivial...
Forum: Homework Help 2021-04-09, 23:14
Replies: 31
Views: 1,258
Posted By charybdis
Wrong. The factors of OP's number are ...

Wrong.

The factors of OP's number are
166447885293942400205064657834447096885456111524808377
1005632514199652040245190989819182186076324308468303514078693528739687994577
(I didn't find these...
Forum: YAFU 2021-04-09, 19:17
Replies: 37
Views: 1,090
Posted By charybdis
tune() doesn't segfault anymore, but I'm still...

tune() doesn't segfault anymore, but I'm still seeing a couple of issues. First it incorrectly detects a 64-bit linux system as 32-bit:
tune_info=Intel(R) Core(TM) i5-8500 CPU @...
Forum: Homework Help 2021-04-09, 12:55
Replies: 31
Views: 1,258
Posted By charybdis
Normally when I stumble across some crap I want...

Normally when I stumble across some crap I want to clean it up, not find its factors.

But if you desperately want to know the factors of this number, the best way is to find them yourself. There's...
Showing results 1 to 25 of 241

 
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