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Forum: Cunningham Tables 2020-08-28, 01:39
Replies: 39
Views: 11,274
Posted By rcv
Thank you, Dr. S. It's probably worth my effort...

Thank you, Dr. S. It's probably worth my effort to understand their paper.

As far as formulae for Homogeneous Cunningham numbers, I've had formulae for the L and M terms for HC numbers up to the...
Forum: Cunningham Tables 2020-08-27, 13:09
Replies: 39
Views: 11,274
Posted By rcv
First, I admit I am having a bit of difficulty...

First, I admit I am having a bit of difficulty with the notation in the 1999 "Chinese paper". What I am wondering is whether or not this paper really describes a "new class" of Aurifeuillian...
Forum: Math 2017-11-08, 14:13
Replies: 54
Views: 3,820
Posted By rcv
First, your approximation formula is OK, only...

First, your approximation formula is OK, only because the numerator is small. A better formula is 1-(279/280)^30=10.2% After you run an additional 65 curves, the chances of having found a factor...
Forum: FactorDB 2017-10-30, 04:12
Replies: 423
Views: 37,088
Posted By rcv
A fun one. And presently the 5th largest in the...

A fun one. And presently the 5th largest in the combined N-1/N+1 category (http://www.factordb.com/nmoverview.php?method=3&digits=2500&perpage=100&skip=0) at factordb.

A 4385-digit number...
Forum: FactorDB 2017-10-28, 04:49
Replies: 423
Views: 37,088
Posted By rcv
The left-hand side of the equation must also be...

The left-hand side of the equation must also be tweaked to represent the sign change in the primitive of k^3q+1 and k^9q+1 (from k^3q-1 and k^9q-1). For each of the binomials in the numerator and...
Forum: FactorDB 2017-10-27, 18:40
Replies: 423
Views: 37,088
Posted By rcv
Following up on my post from a couple of days...

Following up on my post from a couple of days ago...

I don't think I have had a successful N-1 factorization of a primitive from a number of the form k^n+/-1. when 3 is not a divisor of n or if n...
Forum: FactorDB 2017-10-27, 03:39
Replies: 423
Views: 37,088
Posted By rcv
@Chris: Actually, I think that's a clever idea! ...

@Chris: Actually, I think that's a clever idea! Even though you call it "brute force" it's probably faster than asking my computer algebra system to perform the factorization.
Forum: FactorDB 2017-10-26, 01:28
Replies: 423
Views: 37,088
Posted By rcv
Thanks for the pointer! It's printing now. My...

Thanks for the pointer! It's printing now. My search hadn't turned over this paper.

Every distinct exponent has been a significant labor. Constraining myself to the numbers, a^b+/-1, already in...
Forum: FactorDB 2017-10-25, 06:25
Replies: 423
Views: 37,088
Posted By rcv
This is a Cookbook method (sort of) for a certain...

This is a Cookbook method (sort of) for a certain class of primes, often provable by the N-1 method.

Many numbers of the form k^n-1 and k^n+1 have recently been added to FactorDB. The methods of...
Forum: FactorDB 2017-10-21, 13:28
Replies: 423
Views: 37,088
Posted By rcv
I guess I never looked carefully at the...

I guess I never looked carefully at the factorizations of cyclotomic primitives minus 1. The mechanics you showed are simple enough. Thank you.

Here are a few I have performed on FactorDB with...
Forum: ElevenSmooth 2017-10-13, 23:36
Replies: 53
Views: 17,205
Posted By rcv
Thanks for the info! Subsequent to Ryan's p60...

Thanks for the info! Subsequent to Ryan's p60 hit on 2^2800+1 (two posts up), someone reported a p58+p447 split to factordb.com. I presume that was also Ryan?
Forum: FactorDB 2017-10-11, 03:32
Replies: 423
Views: 37,088
Posted By rcv
The number shown by axn doesn't have any...

The number shown by axn doesn't have any algebraic factors because *it* is the primitive factor of 1243^423-1. Is your question a typographical error? Or should we expect the additional "-1" to be...
Forum: FactorDB 2017-10-09, 17:08
Replies: 448
Views: 40,407
Posted By rcv
Ed/Chris: I'm not quite sure how factordb counts...

Ed/Chris: I'm not quite sure how factordb counts new ID's against your limit, but if you are getting a lot of small factors, would it be possible to simply split the 80-100-digit composites into two...
Forum: FactorDB 2017-10-04, 03:54
Replies: 448
Views: 40,407
Posted By rcv
I e-mailed Markus a couple of days ago about the...

I e-mailed Markus a couple of days ago about the massive number of IDs being created. He responded a few hours ago. He has done something to stop the egregious user, but it also seems he has...
Forum: FactorDB 2017-10-02, 13:44
Replies: 67
Views: 6,899
Posted By rcv
Good luck, Chris. But I fear you will never...

Good luck, Chris. But I fear you will never catch up. Below is a sampling of every millionth ID. Number 900000000 was entered on February 2, 2017. Number 950000000 was entered on July 31, 2017. ...
Forum: FactorDB 2017-10-01, 09:19
Replies: 67
Views: 6,899
Posted By rcv
There are tens of thousands of these entries...

There are tens of thousands of these entries (perhaps hundreds of thousands) in the low range of the Unknown numbers. And most of the numbers I see are of the form a^b-1. (Although some are of the...
Forum: FactorDB 2017-09-30, 18:55
Replies: 67
Views: 6,899
Posted By rcv
As you probably know, FactorDB does not have an...

As you probably know, FactorDB does not have an inherent understanding of algebraic factorizations.

About five or six years ago there were many large ElevenSmooth numbers in FactorDB (i.e.,...
Forum: FactorDB 2017-09-30, 13:37
Replies: 1
Views: 935
Posted By rcv
Thank you for a database capable of holding a billion+ numbers

I note that passing of the billionth ID (http://www.factordb.com/index.php?id=1100000001000000000) into FactorDB's "other numbers" range on September 30, 2017, 2:31 pm (database time).

Thank you,...
Forum: Math 2017-09-29, 15:29
Replies: 54
Views: 3,820
Posted By rcv
I stand by my analogy for the purpose of...

I stand by my analogy for the purpose of simplifying the problem so that the OP (and others) might be able to answer their own question. I also assert you are discussing 2nd order effects, which...
Forum: Math 2017-09-29, 14:03
Replies: 54
Views: 3,820
Posted By rcv
Of course, you are right. As long as an...

Of course, you are right. As long as an *average* of 1 in n ECM curves is one of the "lucky curves", and as long as the designer of the ECM program has applied the "common wisdom" in selecting the...
Forum: Math 2017-09-29, 11:08
Replies: 54
Views: 3,820
Posted By rcv
Going back to petrw1's original question. Assume...

Going back to petrw1's original question. Assume the people who wrote your favorite ECM factoring program have done all the nasty math involving the Pi and Dickman's function and have come up with...
Forum: Math 2017-09-26, 05:50
Replies: 36
Views: 4,670
Posted By rcv
[/QUOTE] Thank you, RDS, for the marvelously...

[/QUOTE]

Thank you, RDS, for the marvelously simple condition for when the intrinsic factor occurs!

Also thank you for the information which leads to a clarification to my post #8...
Forum: Data 2017-09-24, 04:09
Replies: 529
Views: 51,917
Posted By rcv
OK. I know how to report a result from prime95. ...

OK. I know how to report a result from prime95. And I know how to report a result from mfactc. But, a brief search did not reveal the trivially simple manual report form, to report a factor, when...
Forum: Math 2017-09-21, 15:53
Replies: 14
Views: 1,224
Posted By rcv
Much of what is being discussed in this thread...

Much of what is being discussed in this thread (and the other thread) mirror the same discussions and pros/cons as for potential Mersenne primes (2^n-1, where n is prime.)

You haven't really made...
Forum: Math 2017-09-20, 11:26
Replies: 36
Views: 4,670
Posted By rcv
I believe the following is correct. But I'm not...

I believe the following is correct. But I'm not a mathematician, so corrections and clarifications are welcome. :smile:

Your example is a special case of the form x^{p\cdot q}-1\text{, where }p...
Showing results 1 to 25 of 143

 
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