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 Showing results 1 to 12 of 12 Search took 0.01 seconds. Search: Posts Made By: princeps
 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: 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...
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