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Forum: Math 2013-06-15, 03:10
Replies: 6
Views: 1,648
Posted By princeps
Generalization of Lucas-Lehmer-Riesel Test...

Generalization of Lucas-Lehmer-Riesel Test (http://numbertheoryapplets.weebly.com/generalization-of-lucas-lehmer-riesel-test.html)
Forum: Information & Answers 2013-03-07, 14:25
Replies: 49
Views: 6,001
Posted By princeps
https://primenumberformula.wordpress.com/

https://primenumberformula.wordpress.com/
Forum: Math 2012-04-10, 05:25
Replies: 4
Views: 863
Posted By princeps
\text{ If } n \equiv 1 \pmod 4 ~\text { and...

\text{ If } n \equiv 1 \pmod 4 ~\text { and }~n\geq1 ~\text { then }~ 5 \mid 2^n+3 , so 5 is only prime number of the form 2^n+3 with property n \equiv 1 \pmod 4

Yes , I mean : S_{i-1} .
Forum: Math 2012-04-10, 05:03
Replies: 4
Views: 863
Posted By princeps
Lucasian Criteria for the Primality of 2^n+3

Definition : Let P_n be a number of the form :

P_n=2^n+3

Definition : Let's define starting seed S as :

S = \begin{cases} 3, & \text{if }n \equiv 0 \pmod 4 \\ 8, & \text{if }n \equiv 2...
Forum: Math 2012-04-02, 12:31
Replies: 15
Views: 4,473
Posted By princeps
As far as I know Inkeri's proof isn't freely...

As far as I know Inkeri's proof isn't freely available...Thanks for your observations..
Forum: Math 2012-04-02, 09:03
Replies: 15
Views: 4,473
Posted By princeps
Yes , you have missed condition : n \geq 2

Yes , you have missed condition : n \geq 2
Forum: Math 2012-04-02, 07:40
Replies: 15
Views: 4,473
Posted By princeps
The tests could be the same only in sense of...

The tests could be the same only in sense of computational complexity , although I think that this test should be faster than Inkeri's . Thank you anyway .
Forum: Math 2012-04-02, 05:20
Replies: 15
Views: 4,473
Posted By princeps
Proof of Primality Test for Fermat Numbers

Let F_n be a Fermat number of the form :

F_n=2^{2^n}+1

Next , let's define sequence S_i as :

S_i=S^4_{i-1}-4\cdot S^2_{i-1}+2 ~ \text { with } ~ S_0=8

Then :
Forum: Miscellaneous Math 2011-11-28, 08:09
Replies: 18
Views: 2,107
Posted By princeps
The another property of prime factor q is : ...

The another property of prime factor q is :

(M_p\equiv0\pmod q \wedge q\equiv 1 \pmod 8) \Rightarrow q\equiv 1 \pmod {8\cdot p}

This can be proved by Fermat's Little Theorem...
Forum: Miscellaneous Math 2011-11-27, 05:33
Replies: 18
Views: 2,107
Posted By princeps
What do you think...Are there more similar...

What do you think...Are there more similar conditions for k ?
Forum: Miscellaneous Math 2011-11-26, 16:47
Replies: 18
Views: 2,107
Posted By princeps
definition of logical conjunction...

definition of logical conjunction (http://en.wikipedia.org/wiki/Logical_conjunction#Definition) which math symbol is : \wedge
Forum: Miscellaneous Math 2011-11-26, 09:55
Replies: 18
Views: 2,107
Posted By princeps
Some Properties of Mersenne Number Factors

M_p=2^p-1

a)

(q=k\cdot 2^3+1 \wedge M_p \equiv 0 \pmod q) \Rightarrow (k\equiv 0 \pmod p \wedge \gcd(k-1,3)=1)

b)

(q=k\cdot 2^3-1 \wedge M_p \equiv 0 \pmod q) \Rightarrow (4 \cdot k\equiv...
Showing results 1 to 12 of 12

 
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