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Search took 0.10 seconds. Search: Posts Made By: charybdis
Forum: Software 2022-06-27, 11:48
Replies: 4
Views: 114
Posted By charybdis
Yes (I assume you meant a(p-1)/2). For k*2^n+1...

Yes (I assume you meant a(p-1)/2). For k*2^n+1 this requires ~n squarings, hence the n iterations that LLR performs.
Forum: Software 2022-06-27, 11:12
Replies: 4
Views: 114
Posted By charybdis
By Euler's criterion...

By Euler's criterion (https://en.wikipedia.org/wiki/Euler%27s_criterion), if p is prime, then a(p-1)/2 is 1 mod p if a is a square mod p, and -1 mod p if a is not a square mod p. So it suffices to...
Forum: NFS@Home 2022-06-26, 23:48
Replies: 141
Views: 16,413
Posted By charybdis
QUEUED AS 2_2694L 2,2694L is another c204...

QUEUED AS 2_2694L

2,2694L is another c204 from the Cunningham project that is ready for GNFS on 16e-small.

n:...
Forum: Miscellaneous Math 2022-06-26, 19:10
Replies: 28
Views: 612
Posted By charybdis
The theorem that says a polynomial has at most as...

The theorem that says a polynomial has at most as many roots as its degree only holds over integral domains, i.e. rings in which it is impossible for two non-zero elements to multiply to zero....
Forum: Miscellaneous Math 2022-06-25, 01:24
Replies: 8
Views: 114
Posted By charybdis
Well apparently they don't. Yafu does: $...

Well apparently they don't. Yafu does:

$ yafu "factor(37598509921358937130067447226996383490394965883350770227491949626316296206227551680872850721799316915254863210166862451532957886446390226981)"...
Forum: Miscellaneous Math 2022-06-24, 23:19
Replies: 8
Views: 114
Posted By charybdis
I used PARI: gp > \p 400 realprecision...

I used PARI:

gp > \p 400
realprecision = 404 significant digits (400 digits displayed)
gp >...
Forum: Miscellaneous Math 2022-06-24, 22:36
Replies: 28
Views: 612
Posted By charybdis
:smile: You might have got this confused...

:smile:

You might have got this confused with the proof that e is irrational, which is much simpler - I seem to recall being set it as an exercise as a first-year undergraduate.
Forum: Miscellaneous Math 2022-06-24, 21:40
Replies: 28
Views: 612
Posted By charybdis
This is the definition of e^11...

This is the definition of e^11...
Forum: Miscellaneous Math 2022-06-24, 21:39
Replies: 8
Views: 114
Posted By charybdis
Fermat's method. It works on the first try.

Fermat's method. It works on the first try.
Forum: MattcAnderson 2022-06-23, 21:52
Replies: 5
Views: 109
Posted By charybdis
If k is odd, then x^k+1 factorizes as...

If k is odd, then x^k+1 factorizes as (x+1)(x^(k-1)-x^(k-2)+...-x+1). Substituting 10^m for x, we see that 10^km+1 is divisible by 10^m+1 if k is odd. In other words, 10^n+1 cannot be prime if n has...
Forum: Factoring 2022-06-22, 16:42
Replies: 501
Views: 76,706
Posted By charybdis
Usual warning that you can't directly compare...

Usual warning that you can't directly compare E-scores for polys with different degrees. Lower degrees overpeform their scores, higher degrees underperform.
Forum: Factoring 2022-06-22, 14:35
Replies: 501
Views: 76,706
Posted By charybdis
Correct for the second one, but not the first. ...

Correct for the second one, but not the first.
288 = 2*3*47, so 13^288+1 has algebraic factors 13^94+1 and 13^6+1, which themselves share a common factor 13^2+1. We can't pull out both algebraic...
Forum: Factoring 2022-06-22, 13:03
Replies: 501
Views: 76,706
Posted By charybdis
Yes, both exponents are divisible by 3 so you can...

Yes, both exponents are divisible by 3 so you can divide out the algebraic factors 13^94+1 and 13^96+1 respectively. So you have to multiply the size of the number by 2/3 to get the actual difficulty.
Forum: NFS@Home 2022-06-15, 16:47
Replies: 62
Views: 4,272
Posted By charybdis
Yes. More relations = more time spent in...

Yes. More relations = more time spent in duplicate, singleton and clique removal.
Forum: FactorDB 2022-06-15, 15:16
Replies: 561
Views: 105,428
Posted By charybdis
It is his current address. He probably didn't...

It is his current address. He probably didn't reply to you because your suggestions were unnecessary and/or stupid.
Forum: Msieve 2022-06-13, 18:55
Replies: 2,217
Views: 221,435
Posted By charybdis
2,2694L

Ran up to admax=50M. These aren't quite Gimarel-standard but they're okay:

n:...
Forum: Cunningham Tables 2022-06-12, 16:10
Replies: 26
Views: 10,735
Posted By charybdis
Hmmm, can you point me to a reference for this?...

Hmmm, can you point me to a reference for this? Surely the optimum ratio is implementation dependent?
Forum: Aliquot Sequences 2022-06-12, 14:14
Replies: 1,718
Views: 198,315
Posted By charybdis
The other consequence of the (b^n-1)/(b-1)...

The other consequence of the (b^n-1)/(b-1) observation is, of course, that SNFS can be used on term 1 for prime bases.
Forum: Aliquot Sequences 2022-06-12, 13:26
Replies: 1,718
Views: 198,315
Posted By charybdis
If the base b is prime, then term 1 of sequence...

If the base b is prime, then term 1 of sequence b^n will be b^(n-1) + b^(n-2) + ... + b + 1 = (b^n-1)/(b-1). Since b^n-1 divides all numbers of the form b^kn-1, this naturally leads to shared factors...
Forum: Msieve 2022-06-09, 17:25
Replies: 2,217
Views: 221,435
Posted By charybdis
Gonna do some CADO polyselect on 2,2694L c204....

Gonna do some CADO polyselect on 2,2694L c204. P=5M, incr=420, starting at admin=5M, haven't decided how far I'll go.
Forum: Factoring 2022-06-09, 16:38
Replies: 12
Views: 587
Posted By charybdis
CADO-NFS should run on a Mac (edit: possibly not...

CADO-NFS should run on a Mac (edit: possibly not an ARM one?), though I have no experience in this regard. The readme contains some specifics about installation on Macs, e.g. needing to install wget...
Forum: Factoring 2022-06-09, 01:44
Replies: 68
Views: 1,396
Posted By charybdis
Not an electrical engineer so I have no clue what...

Not an electrical engineer so I have no clue what you're on about.
Unless this is just chalsall code for "are you an electrical engineer?" in which case you've got your answer.



Never mind...
Forum: Factoring 2022-06-09, 00:41
Replies: 68
Views: 1,396
Posted By charybdis
I don't know where you're getting the term...

I don't know where you're getting the term "exclusion" from. It's an instruction to GMP-ECM saying "I've already run stage 1 with B1=8e8, so please run stage 2 with the appropriate B2".



Excuse...
Forum: NFS@Home 2022-06-08, 18:12
Replies: 20
Views: 565
Posted By charybdis
Yeah, you'll be fine. As a rule of thumb, matrix...

Yeah, you'll be fine. As a rule of thumb, matrix solving time roughly multiplies by 4.5 for each doubling of the matrix dimensions.
Forum: Factoring 2022-06-08, 17:13
Replies: 68
Views: 1,396
Posted By charybdis
What exactly were you trying to do?...

What exactly were you trying to do? "B1=50000000-49000000" is totally meaningless from a theoretical point of view. Why would anyone even think of trying it?

And what do you mean by an exclusion??...
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