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Search: Posts Made By: kijinSeija
Forum: Miscellaneous Math 2021-12-07, 17:50
Replies: 9
Views: 165
Posted By kijinSeija
I observed new things about 3*2^q-1 and 3*2^q+1...

I observed new things about 3*2^q-1 and 3*2^q+1 with the same seed S(0) = 2/3 and S(i+1) = S(i)^2-2

Let Rq = 3*2^q-1 and Pq = 3*2^q+1

Rq or Pq is prime iff S(q-1) = 2 or Rq - 1 (or Pq - 1) (mod...
Forum: Miscellaneous Math 2021-12-05, 23:47
Replies: 9
Views: 165
Posted By kijinSeija
With this formula, I haven't the Carmichael...

With this formula, I haven't the Carmichael numbers at least the 8911 one


T(q)={Wq=557*2^q-1;S0=2^557;S=S0;print("q= ",q);for(i=1,q-1,S=Mod(S^2,Wq));if(S==2,print("prime"))}


For the Riesel...
Forum: Miscellaneous Math 2021-12-05, 22:22
Replies: 9
Views: 165
Posted By kijinSeija
Oh thanks for your quick reply so it definitely...

Oh thanks for your quick reply so it definitely doesn't work for Proth prime :(
Forum: Miscellaneous Math 2021-12-05, 22:06
Replies: 9
Views: 165
Posted By kijinSeija
Oh I see I forgot to check Carmichael numbers. I...

Oh I see I forgot to check Carmichael numbers. I forgot to say than k>1, n>1 and q>1 otherwise you can get false positive but maybe it is not enough to avoid Carmichael numbers :/
Forum: Miscellaneous Math 2021-12-05, 21:28
Replies: 9
Views: 165
Posted By kijinSeija
Primality test for Riesel and Proth prime ?

Here is what I observed :

For Riesel prime :

Let Rq = k*n^q-1, S(0) = n^k and S(i+1)= S(i)^n

Rq is prime iff S(q) = n^2

For example with 10*11^3-1, S(0)=11^10 and S(i+1) = S(i)^11
Forum: Wagstaff PRP Search 2021-11-27, 13:43
Replies: 7
Views: 825
Posted By kijinSeija
For the repunits test. I use...

For the repunits test. I use T(q)={Wq=(10^q-1)/9;S0=q^10;S=S0;print("q= ",q);for(i=1,q-1,S=Mod(S^10,Wq));if(S==S0,print("prime"))}
forprime(n=3,1050,T(n)) on Pari Gp and I found for q prime : 3, 19,...
Forum: Wagstaff PRP Search 2021-11-26, 20:47
Replies: 7
Views: 825
Posted By kijinSeija
I try some new seeds and I found this : Let...

I try some new seeds and I found this :

Let Wq=(2^q+1)/3, S0=q^2, and: S(i+1)=Si² (mod Wq)

Wq is a prime iff: Sq−1 ≡ S0 (mod Wq)

I tried until p<1000 and I found only Wagstaff prime

I...
Forum: Wagstaff PRP Search 2021-11-26, 13:12
Replies: 7
Views: 825
Posted By kijinSeija
Thanks for your reply :) Unfortunately, I'm...

Thanks for your reply :)

Unfortunately, I'm not a mathematician so I think it could be impossible for me to prove it. I try to understand the proof of the Lucas-Lehmer test and trying to transpose...
Forum: Wagstaff PRP Search 2021-11-25, 17:46
Replies: 7
Views: 825
Posted By kijinSeija
Minus A new Wagstaff primality test ?

Let Wq=(2^q+1)/3, S0=(2^(q-2)+1)/3, and: Si+1=S2i−2 (mod Wq)

Wq is a prime iff: Sq−1 ≡ S0 (mod Wq)

I used this code on PariDroid (thanks to T.Rex) to check with some prime numbers and it seems...
Forum: Wagstaff PRP Search 2021-09-20, 18:58
Replies: 5
Views: 7,579
Posted By kijinSeija
(3+sqrt(-7/4))*(3-sqrt(-7/4)) = 43/4 right ? I'm...

(3+sqrt(-7/4))*(3-sqrt(-7/4)) = 43/4 right ? I'm not sure about that
Forum: Math 2021-05-23, 17:09
Replies: 42
Views: 6,277
Posted By kijinSeija
I mean you can find three random numbers (a, b,...

I mean you can find three random numbers (a, b, c) that respect that :

a+b+c = 2^n-1
and a²+b²+c²=(4^n-1)/3

If a+b+c is a prime Mersenne number.

you can't find any numbers for example for...
Forum: Math 2021-05-23, 15:32
Replies: 42
Views: 6,277
Posted By kijinSeija
Hi and thanks for your reply. And by the way...

Hi and thanks for your reply.

And by the way I noticed something interesting : if a+b+c = 2^n-1 you can found number with a²+b²+c² = (4^n-1)/3 and it seems it works with Mersenne number (it seems...
Forum: Math 2021-03-21, 16:14
Replies: 42
Views: 6,277
Posted By kijinSeija
Hi I would like to know if a^(2^n) mod...

Hi

I would like to know if a^(2^n) mod (2^n-1) = a² when a is between 0 and sqrt(2^n-1) and a is an integer when 2^n-1 is prime and only if it's prime ?

I tried this with some Mersenne...
Showing results 1 to 13 of 13

 
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