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 Showing results 1 to 14 of 14 Search took 0.01 seconds. Search: Posts Made By: jfollas
 Forum: Lounge 2005-03-06, 16:38 Replies: 43 Views: 2,874 Posted By jfollas 29619697 29619697
 Forum: Math 2004-09-11, 12:51 Replies: 37 Views: 4,278 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 Views: 4,278 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 Views: 1,719 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 Views: 769 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 Views: 769 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 Views: 3,849 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 Views: 42,432 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 Views: 1,166 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 Views: 42,432 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 Views: 2,046 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 Views: 947 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 Views: 947 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 Views: 947 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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