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Forum: And now for something completely different 2021-12-16, 00:43
Replies: 151
Views: 36,353
Posted By maxal
Btw, a general formula of this kind is given in...

Btw, a general formula of this kind is given in Theorem 4.4 a recent preprint (https://arxiv.org/abs/2004.14000). It also shows how to efficiently compute the constant ala [$]C_6[/$] modulo a given...
Forum: FactorDB 2017-11-14, 04:16
Replies: 1
Views: 2,929
Posted By maxal
bugreport: duplicate entries

These two entries seem to correspond to the same number:
http://factordb.com/index.php?showid=1100000000900935563
http://factordb.com/index.php?showid=1100000000902314000

Also, while this number...
Forum: Factoring 2013-12-09, 16:43
Replies: 10
Views: 3,036
Posted By maxal
To eliminate obvious cases with no solutions, I...

To eliminate obvious cases with no solutions, I suggest first to compute the multiplicative order $q$ (by factoring p-1 and eliminating its prime divisors as needed) of \alpha and test whether...
Forum: Puzzles 2013-10-10, 04:17
Replies: 10
Views: 3,276
Posted By maxal
If anybody still cares, here is a preprint about...

If anybody still cares, here is a preprint about solving Tower of Hanoi with random moves:
http://arxiv.org/abs/1304.3780
Forum: Wagstaff PRP Search 2013-10-10, 01:23
Replies: 7
Views: 11,055
Posted By maxal
It may be worth to point out the previous...

It may be worth to point out the previous discussion on this topic inspired by Anton Vrba's proposed proof: http://www.mersenneforum.org/showthread.php?t=10737
Forum: Factoring 2013-10-09, 17:48
Replies: 527
Views: 115,667
Posted By maxal
I've just got factorization of 102^103 + 1 =...

I've just got factorization of 102^103 + 1 = 103^2 * prp74 * prp130 with SNFS:
prp74 factor: 16577923085747542727498881886756397313868752518022676502052070512564532587
prp130 factor:...
Forum: Factoring 2013-10-07, 01:24
Replies: 10
Views: 3,036
Posted By maxal
See also http://www.cs.toronto.edu/~cvs/dlog/

See also http://www.cs.toronto.edu/~cvs/dlog/
Forum: FactorDB 2012-02-13, 04:06
Replies: 1,627
Views: 195,825
Posted By maxal
It would be nice if the engine was able to figure...

It would be nice if the engine was able to figure that out automatically. If I use it for factoring, I do not want to care about relationship of the input number to other numbers in the database, I...
Forum: FactorDB 2012-02-13, 02:22
Replies: 1,627
Views: 195,825
Posted By maxal
factordb may return incomplete factorization of a...

factordb may return incomplete factorization of a proper factor of a completely factored number.

E.g., for 10^486 - 1 it returns complete factorization (FF status), while for (10^486-1)/487 it...
Forum: Computer Science & Computational Number Theory 2012-01-31, 16:09
Replies: 138
Views: 21,277
Posted By maxal
should be ((p-1)!+1)/p \equiv H_{n-1} \pmod{p}...

should be ((p-1)!+1)/p \equiv H_{n-1} \pmod{p} for the order n generalized Wilson prime. So order 1 generalized Wilson primes are conventional Wilson primes, order 2 generalized Wilson primes are...
Forum: Computer Science & Computational Number Theory 2012-01-31, 12:48
Replies: 138
Views: 21,277
Posted By maxal
This is a nice search project. Do you maintain...

This is a nice search project. Do you maintain database of Wilson quotients modulo p in the search?
They would be helpful in finding other related primes such as generalized Wilson primes p of order...
Forum: FactorDB 2011-09-10, 19:22
Replies: 1,627
Views: 195,825
Posted By maxal
Is there a way to get the factorization of a...

Is there a way to get the factorization of a given number from factordb.com in plain text format to simplify parsing the result by a script?
Forum: Math 2011-03-14, 11:41
Replies: 43
Views: 4,476
Posted By maxal
That's easy to prove. Assume that...

That's easy to prove.
Assume that q=\gcd(2^a+2^b,n)>1. Since p is an odd prime and 2^p \equiv 1\pmod{q}, we have that 2^k \not\equiv -1\pmod{q} for all k. On the other hand, 2^a+2^b\equiv 0\pmod{q}...
Forum: Math 2010-10-13, 20:07
Replies: 44
Views: 6,008
Posted By maxal
Here are some more terms: 5, 29, 2045, 40133,...

Here are some more terms:
5, 29, 2045, 40133, 971837, 5063357, 7354397, 16554917, 17786525, 42244637, 52717277, 79704029, 84896957, 153424637, 262984997, 288644957, 328721213, 350252957, 353294757,...
Forum: Software 2010-10-04, 17:11
Replies: 18
Views: 2,365
Posted By maxal
I don't, the arithmetic progression (that is, the...

I don't, the arithmetic progression (that is, the constants A and B) is given.
Forum: Software 2010-10-04, 16:30
Replies: 18
Views: 2,365
Posted By maxal
In general we can assume L=1. The order of U/A...

In general we can assume L=1. The order of U/A (notice that the "step" A may be large, making it possible to reach larger U) is reasonable - 10^20 or so, as you mentioned. And, indeed, the sieve may...
Forum: Software 2010-10-03, 17:38
Replies: 18
Views: 2,365
Posted By maxal
That may be a good idea, if there is no...

That may be a good idea, if there is no ready-to-use tool.
Another option is to adapt the PrimeGen tool http://cr.yp.to/primegen.html that uses sieve of Atkin.
Forum: Software 2010-10-03, 17:13
Replies: 18
Views: 2,365
Posted By maxal
AP26 is irrelevant. I'm not looking for primes...

AP26 is irrelevant. I'm not looking for primes forming an arithmetic progression, but primes in the given arithmetic progression (possibly with gaps between them). The latter problem is much simpler...
Forum: Software 2010-10-02, 17:23
Replies: 18
Views: 2,365
Posted By maxal
science_man_88, I asked concrete question about...

science_man_88, I asked concrete question about the software - if you don't know the answer, please don't make irrelevant comments.
And please don't teach me the theory - believe me, I know it well.
Forum: Software 2010-10-02, 16:40
Replies: 18
Views: 2,365
Posted By maxal
I'm not asking about the theory, I'm asking about...

I'm not asking about the theory, I'm asking about the _software_.
Forum: Software 2010-10-02, 14:14
Replies: 18
Views: 2,365
Posted By maxal
sieving primes in arithmetic progressions

Does there exist a fast optimized siever for finding primes in a given arithmetic progression?

That is, for given the parameters A, B along with the range [L,U], such siever should find and report...
Forum: FactorDB 2010-09-21, 01:06
Replies: 1,627
Views: 195,825
Posted By maxal
Here is a new version that supports both msieve...

Here is a new version that supports both msieve and yafu:

#!/usr/bin/perl
use strict;

print("FactorDB Helper 1.5\n");

# wget executable
my $wget = "wget --no-check-certificate";
Forum: FactorDB 2010-09-20, 21:54
Replies: 1,627
Views: 195,825
Posted By maxal
It now works. Thanks! Here is an updated...

It now works. Thanks!

Here is an updated script that uses new features.

#!/usr/bin/perl
use strict;

print("FactorDB Helper 1.3\n");

# wget executable
Forum: FactorDB 2010-09-20, 21:44
Replies: 1,627
Views: 195,825
Posted By maxal
http://factordb.com/getrandom.php?n=100&t=3...

http://factordb.com/getrandom.php?n=100&t=3 produces an empty page ;(
Forum: FactorDB 2010-09-20, 21:27
Replies: 1,627
Views: 195,825
Posted By maxal
Thanks, that's helpful But n=100 seems to...

Thanks, that's helpful
But n=100 seems to produce only a couple of dozens id's ;(
Also, parameter maxdig would be helpful to avoid factorization of monsters.

On a different topic, could you...
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