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Search took 0.01 seconds. Search: Posts Made By: jfollas

Forum: Lounge

2005-03-06, 16:38

Replies: 43

Poll: Poll: When Will M43 Be Discovered?

Views: 3,662

Posted By jfollas

29619697

29619697

Forum: Math

2004-09-11, 12:51

Replies: 37

General Solution to Polynomial Equations

Views: 6,357

Posted By jfollas

What stuck in my mind was that when you multiply...

What stuck in my mind was that when you multiply using FFT, you first represent the number as a polynomial equation:

57829 = 5x^4 + 7x^3 + 8x^2 + 2x + 9

I wasn't sure if the roots of such an...

Forum: Math

2004-09-10, 14:18

Replies: 37

General Solution to Polynomial Equations

Views: 6,357

Posted By jfollas

General Solution to Polynomial Equations

What are the implications for factoring/primality testing (if any) of the newly announced general solution to polynomial equations? This piqued my interest because I remembered something about FFT...

Forum: Miscellaneous Math

2004-08-18, 15:45

Replies: 16

LL test speed up?

Views: 2,540

Posted By jfollas

Well, that's an important discovery that I made...

Well, that's an important discovery that I made earlier this year and have been developing ever since.... I call this "Shortcutting the Lucas-Lehmer Test" because all you need to do is prove that...

Forum: Math

2004-08-01, 19:07

Replies: 3

Can LL residue hit zero before the last iteration?

Views: 1,470

Posted By jfollas

I've studied the Lucas-Lehmer sequence quite a...

I've studied the Lucas-Lehmer sequence quite a bit over the past year, and based on all of the empirical evidence that I've collected, I have concluded that the LL sequence will zero out after any...

Forum: Math

2004-08-01, 12:12

Replies: 3

Can LL residue hit zero before the last iteration?

Views: 1,470

Posted By jfollas

The LL test will zero out for a prime number Mp...

The LL test will zero out for a prime number Mp on step P-1 if the starting term is from the sequence:

A(0)=4, A(1)=52, A(n)=(14*A(n-1) - A(n-2)) mod Mp [Sloane A018844]

It is possible that...

Forum: Software

2004-07-31, 14:51

Replies: 27

How does this whole prime-testing thing work?

Views: 4,961

Posted By jfollas

Common question... Depends what step you're on. ...

Common question... Depends what step you're on.

In the beginning, Prime95 tries to find small factors of the prime using several different methods. If a small factor is found, then Prime95...

Forum: Math

2004-07-30, 15:11

Replies: 61

Sticky: FFT explanation for non math guys

Views: 69,004

Posted By jfollas

Is there a FFT implementation that would be...

Is there a FFT implementation that would be better suited for repeatedly performing the multiplication step while remaining in the transform (i.e., where precision errors are not an issue), or at...

Forum: Math

2004-07-30, 02:44

Replies: 2

Equality of quadratic equations

Views: 1,582

Posted By jfollas

Check out Dario Alpern's "Generic Two Integer...

Check out Dario Alpern's "Generic Two Integer Variable Equation Solver":

http://www.alpertron.com.ar/QUAD.HTM

He offers a lot of background information about this subject.

BTW: You might not...

Forum: Math

2004-07-29, 13:58

Replies: 61

Sticky: FFT explanation for non math guys

Views: 69,004

Posted By jfollas

I'm still trying to get my head around...

I'm still trying to get my head around multiplying using FFT's, but I have a couple questions that popped up:

As I understand, to multiply using FFT, you need to do a transform, perform the...

Forum: Math

2004-07-21, 17:45

Replies: 7

A new Mersenne conjecture: roots of Lucas-Lehmer test.

Views: 3,074

Posted By jfollas

I apologize if this is repeated information, but...

I apologize if this is repeated information, but I haven't specifically seen it posted anywhere.

I did some studying of the "roots of LLT", specifically around Sloane's A018844:
...

Forum: Math

2004-07-02, 22:26

Replies: 3

Raising numbers to a power of two

Views: 1,909

Posted By jfollas

Hmm, it seems that your explaination works great...

Hmm, it seems that your explaination works great for the case where the modulus is less than the exponent as in the example 37^1024 (mod 127). Thanks for the details, since I haven't seen that...

Forum: Math

2004-07-02, 22:01

Replies: 3

Raising numbers to a power of two

Views: 1,909

Posted By jfollas

By Mersenne, I simply meant any number in the...

By Mersenne, I simply meant any number in the form of 2^P-1, be it a prime or composite (though primality not necessarily known at the evaluation time).

Forum: Math

2004-07-02, 13:18

Replies: 3

Raising numbers to a power of two

Views: 1,909

Posted By jfollas

Raising numbers to a power of two

Are there any shortcuts for raising a number to a power of two (modulo a mersenne)?

Examples:

37^1024 (mod 127)

65^2048 (mod 8191)

I realize that the exponential operation using the...

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