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Forum: Math 2016-04-03, 10:01
Replies: 12
Views: 3,889
Posted By primus
http://math.stackexchange.com/q/1721415

http://math.stackexchange.com/q/1721415
Forum: Math 2016-03-29, 14:18
Replies: 12
Views: 3,889
Posted By primus
http://math.stackexchange.com/q/1718453

http://math.stackexchange.com/q/1718453
Forum: Miscellaneous Math 2015-09-16, 17:49
Replies: 27
Views: 3,159
Posted By primus
http://math.stackexchange.com/q/1426586

http://math.stackexchange.com/q/1426586
Forum: Miscellaneous Math 2015-09-02, 09:26
Replies: 38
Views: 3,353
Posted By primus
My unproven solution : For n>10 and n is...

My unproven solution :

For n>10 and n is even .

PPT(n)=
{
my(s=Mod(6,(2^n+5)/3));
for(i=1,n-1,s=s^2-2);
s==6
}
Forum: Miscellaneous Math 2015-09-01, 13:13
Replies: 10
Views: 1,134
Posted By primus
My solution : For n>10 and n is odd . ...

My solution :

For n>10 and n is odd .

PPT(n)=
{
my(s=Mod(6,(2^n-5)/3));
for(i=1,n-1,s=s^2-2);
s==2*polchebyshev(4,1,3)
}
Forum: Miscellaneous Math 2015-07-04, 12:44
Replies: 14
Views: 1,546
Posted By primus
http://arxiv.org/pdf/1506.03444.pdf

http://arxiv.org/pdf/1506.03444.pdf
Forum: Miscellaneous Math 2015-03-20, 15:09
Replies: 1
Views: 1,073
Posted By primus
Pseudoprimality Hypothesis for Specific Class of Generalized Fermat Numbers

Definition

Let P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right) , where m and x are nonnegative integers .

Conjecture

Let F_n(b)=b^{2^n}+1 such...
Forum: Miscellaneous Math 2015-03-20, 14:20
Replies: 14
Views: 1,546
Posted By primus
Thanks Darth Vader for changing a title .

Thanks Darth Vader for changing a title .
Forum: Miscellaneous Math 2015-03-18, 13:06
Replies: 14
Views: 1,546
Posted By primus
Let P_m(x)=2^{-m}\cdot...

Let P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right) , where m and x are nonnegative integers .

Let N=k\cdot b^n-1 such that n>2 , k<b^n and
...
Forum: Miscellaneous Math 2014-12-16, 08:54
Replies: 14
Views: 1,546
Posted By primus
Reference : D. H. Lehmer, "An extended...

Reference :

D. H. Lehmer, "An extended theory of Lucas' functions," Ann. of Math., v. 31, 1930, pp.419-448.
Forum: Miscellaneous Math 2014-12-14, 17:28
Replies: 14
Views: 1,546
Posted By primus
P_3(x)=5778 Find x ? You can find more...

P_3(x)=5778
Find x ?

You can find more informations in this article (http://en.wikipedia.org/wiki/Talk:Lucas%E2%80%93Lehmer%E2%80%93Riesel_test).
Forum: Miscellaneous Math 2014-12-14, 14:24
Replies: 14
Views: 1,546
Posted By primus
Finding the starting value ....

Finding the starting value . (http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test#Finding_the_starting_value)
Forum: Miscellaneous Math 2014-12-09, 11:00
Replies: 14
Views: 1,546
Posted By primus
Lucasian Pseudoprimality Hypothesis for Specific Class of k 2^n-1

Please delete this post if this generalization is already known .

Definition

Let P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right) , where m and x...
Forum: Miscellaneous Math 2014-10-12, 09:10
Replies: 1
Views: 1,668
Posted By primus
Conjectured Primality Test for Specific Class of Mersenne Numbers

Conjecture

Let M_p=2^p-1 such that p is prime and p\equiv 5 \pmod{6}

Let S_i=S_{i-1}^8-8\cdot S_{i-1}^6+20\cdot S_{i-1}^4-16 \cdot S_{i-1}^2+2 with S_0=4 , then

M_p is prime iff S_{(p-2)/3}...
Forum: Programming 2014-09-22, 11:26
Replies: 13
Views: 2,440
Posted By primus
I think that c/c++ implementation with adequate...

I think that c/c++ implementation with adequate libraries for fast multiplication should be faster than llr .
This java implementation is for demonstration purposes only .
Wish you the best of...
Forum: Programming 2014-09-20, 15:19
Replies: 13
Views: 2,440
Posted By primus
See Theorem 3.1...

See Theorem 3.1 (http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=57999AA11750B887F48931B7C2070A9E?doi=10.1.1.386.7092&rep=rep1&type=pdf)
Forum: Programming 2014-09-20, 05:29
Replies: 13
Views: 2,440
Posted By primus
About The Ig Nobel Prizes...

About The Ig Nobel Prizes (http://www.improbable.com/ig/)
Forum: Programming 2014-09-19, 06:02
Replies: 13
Views: 2,440
Posted By primus
Prothon

Java implementation of Lucasian primality test for specific classes of Proth numbers . (https://github.com/MartinMystery/Prothon)
Forum: Computer Science & Computational Number Theory 2014-08-21, 15:16
Replies: 8
Views: 2,423
Posted By primus
Thanks for help and references ! :bow:

Thanks for help and references ! :bow:
Forum: Computer Science & Computational Number Theory 2014-08-16, 05:35
Replies: 8
Views: 2,423
Posted By primus
Can you find counterexample for 5\not\mid b ?

Can you find counterexample for 5\not\mid b ?
Forum: Computer Science & Computational Number Theory 2014-08-15, 13:27
Replies: 8
Views: 2,423
Posted By primus
I started a new thread because this conjecture...

I started a new thread because this conjecture uses 4 for starting value , not 3 , as you noticed , and that's why it couldn't be named as generalization of the conjecture for k\cdot 6^n-1 . This is...
Forum: Computer Science & Computational Number Theory 2014-08-15, 05:33
Replies: 8
Views: 2,423
Posted By primus
Disproven Primality Test for Specific Class of kb^n-1

Definition : \text{Let} P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right) , \text{where} m \text{and} x \text{are nonnegative integers .}

Conjecture :...
Forum: Computer Science & Computational Number Theory 2014-08-14, 14:59
Replies: 16
Views: 3,782
Posted By primus
\text{For} k \in [1 , 109] \text{with} n \in [3 ,...

\text{For} k \in [1 , 109] \text{with} n \in [3 , 300]

maxima code to test this conjecture :

/* n>2 , k=3,9(mod 10) , k<b^n */
k:109;
for n from 3 thru 300 do...
Forum: Computer Science & Computational Number Theory 2014-08-14, 05:45
Replies: 16
Views: 3,782
Posted By primus
Conjectured Primality Test for Specific Class of k6^n-1

Definition : \text{Let} $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right) , \text{where} m \text{and} x \text{are nonnegative integers .}
...
Forum: Math 2014-08-08, 20:05
Replies: 46
Views: 11,503
Posted By primus
Conjectured Polynomial Time Primality Tests for...

Conjectured Polynomial Time Primality Tests for Numbers of Special Forms (https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxwZWRqYXByaW11c3xneDoyN2Q1OGI1N2ZhMGY5MWZj)
Showing results 1 to 25 of 26

 
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