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Search: Posts Made By: kijinSeija
Forum: Wagstaff PRP Search 2022-08-25, 13:22
Replies: 20
Views: 6,202
Posted By kijinSeija
New formula

I checked with this formula

$\omega = (\frac{1}{2} (1 + i \sqrt7))^{(\frac{2^{p - 1} - 1}{3})} + (\frac{1}{2} (1 - i \sqrt7))^{(\frac{2^{p - 1} - 1}{3})}$

And it seems than $\omega \equiv 0...
Forum: Wagstaff PRP Search 2022-08-21, 18:53
Replies: 20
Views: 6,202
Posted By kijinSeija
Inspired by Reix conjecture, I think I found a...

Inspired by Reix conjecture, I think I found a formula that divides only Wagstaff primes numbers and not the composite Wagstaff numbers :

The formula is :

G_n = 4^{2^n} \cdot ((1/8 - 1/8 (3 i...
Forum: Wagstaff PRP Search 2022-08-20, 21:23
Replies: 20
Views: 6,202
Posted By kijinSeija
Talking New property ?

Maybe I found a new property about the Reix conjecture :

Let W_p = (2^p+1)/3 where p is a prime number >3

Let the sequence S_i = S_{i-1}^2-2 with S_0 = 1/4 = (2^{(p-2)}+1)/3

W_p is prime if...
Forum: Miscellaneous Math 2022-08-17, 12:11
Replies: 1
Views: 154
Posted By kijinSeija
Mistake in OEIS ?

Hi,

I'm not sure but I think I found a little mistake in OEIS at https://oeis.org/A331038

Not in the sequence but in the comments about Lucas-Lehmer test it say than :



The methods works...
Forum: Wagstaff PRP Search 2022-08-15, 21:15
Replies: 20
Views: 6,202
Posted By kijinSeija
S_{0} = 7 not 3 sorry for the mistake

S_{0} = 7 not 3 sorry for the mistake
Forum: Wagstaff PRP Search 2022-08-15, 15:47
Replies: 20
Views: 6,202
Posted By kijinSeija
For Wagstaff Numbers : ?...

For Wagstaff Numbers :


? forprime(q=3,200, print(t(q)))
q:3 ,w: 3
s1=0

q:5 ,w: 11
s1=0
Forum: Wagstaff PRP Search 2022-08-14, 15:37
Replies: 20
Views: 6,202
Posted By kijinSeija
Maybe I found a probable primality test than...

Maybe I found a probable primality test than works for Wagstaff and Mersenne primes with the same conditions :

Let $N = \frac{-a^p-1}{-a-1}$ with a = 2 for Wagstaff numbers and a= -2 for Mersenne...
Forum: Dobri 2022-08-08, 12:10
Replies: 75
Views: 7,154
Posted By kijinSeija
Ok thanks for your answer I understand a little...

Ok thanks for your answer I understand a little more now. :grin:

Do you think you can prove the same thing about Wagstaff composite numbers ?

I found than if 8p+1 = 256a^2+(2*b-1)^2 and p and...
Forum: Dobri 2022-08-06, 15:49
Replies: 75
Views: 7,154
Posted By kijinSeija
Hi, I noticed something about the prime of...

Hi,

I noticed something about the prime of the form p and 8p+1 and their divisibility by 2^p-1

If p = ((2a-1)^2+64(2b-1)^2-1)/8 and 8p+1 = (2a-1)^2+64(2b-1)^2, then 8p+1 divides 2^p-1

To...
Forum: Factoring 2022-07-30, 16:17
Replies: 106
Views: 8,475
Posted By kijinSeija
Ok I thought than M1277 can't be write as...

Ok I thought than M1277 can't be write as a^2+3b^2 because I checked that with WolframAlpha but I didn't know than you need at least one known prime factor for that. Thanks for your answer !
Forum: Factoring 2022-07-30, 15:51
Replies: 106
Views: 8,475
Posted By kijinSeija
You can't write 2^1277-1 as a^2+3b^2 so it means...

You can't write 2^1277-1 as a^2+3b^2 so it means than all factors of M1277 are == 2 (mod 3) ? And I have seen on this link https://oeis.org/A215799 than prime factors of 2^p-1 which are == 2 (mod 3)...
Forum: Math 2022-06-12, 20:37
Replies: 3
Views: 2,177
Posted By kijinSeija
I don't know if it's related to this topic but I...

I don't know if it's related to this topic but I made some probable primality test for numbers of the forum (a^p-1)/(a-1) and (a^p+1)/(a+1) using Chebyshev polynomials :

but the test isn't perfect...
Forum: Math 2022-05-13, 20:32
Replies: 0
Views: 585
Posted By kijinSeija
Probable primality test for numbers of the form (10^n-1)/9-2 and (10^n+1)/11-2 ?

Here is what I observed :

For (10^n−1)/9 - 2 :

Let the sequence Si=S^10(i-1)−10*S^8(i−1)+35*S^6(i−1)−50*S^4(i−1)+25*S^2(i−1)−2 with S0=123. Then N is prime if and only if Sn−1≡710647 (modN).
...
Forum: And now for something completely different 2022-04-30, 21:23
Replies: 6
Views: 649
Posted By kijinSeija
thanks for your help and for the address :grin:

thanks for your help and for the address :grin:
Forum: And now for something completely different 2022-04-30, 19:39
Replies: 6
Views: 649
Posted By kijinSeija
(((30809^30809)%30809#)/30809) is 3-PRP! ...

(((30809^30809)%30809#)/30809) is 3-PRP!
(((42017^42017)%42017#)/42017) is 3-PRP!
Forum: And now for something completely different 2022-04-30, 16:12
Replies: 6
Views: 649
Posted By kijinSeija
Primes of the form ((p^p)%p#)/p

Have these kinds of prime numbers been studied ?

I found nothing on factordb and OEIS.

I use the % for the modulo operation and # for the primorial numbers.

I used PFGW and I found these...
Forum: Dobri 2022-04-20, 10:57
Replies: 75
Views: 7,154
Posted By kijinSeija
Yes of course 6*p+1 must be prime I guess but p...

Yes of course 6*p+1 must be prime I guess but p isn't necessary prime.

For example : (6*21+1) = 127 divides (2^21-1) but 21 isn't prime.
Forum: Dobri 2022-04-20, 08:44
Replies: 75
Views: 7,154
Posted By kijinSeija
Like Mersenne composites, it seems than p == 3...

Like Mersenne composites, it seems than p == 3 (mod 4) and 6*p+1 = 27a^2+16b^2 should be the two condition for 6p+1 divides Wagstaff numbers (2^p+1)/3. (7, 47, 83, 107, 263, 271 ...) The sequence...
Forum: Dobri 2022-04-20, 07:54
Replies: 75
Views: 7,154
Posted By kijinSeija
Thanks, this is interesting. How do you check...

Thanks, this is interesting. How do you check that ? With Wolfram Alpha ?
Forum: Dobri 2022-04-20, 07:18
Replies: 75
Views: 7,154
Posted By kijinSeija
But 31 divides 31 for example. This is really a...

But 31 divides 31 for example. This is really a counterexample ?

Oh I see what you mean :grin:
Forum: Dobri 2022-04-19, 18:48
Replies: 75
Views: 7,154
Posted By kijinSeija
So if we add than p == 1 (mod 4) and 6*p+1 =...

So if we add than p == 1 (mod 4) and 6*p+1 = 27a^2+b^2 should be the two conditions for 6*p+1 divides 2^p-1 right ?
Forum: Dobri 2022-04-18, 16:41
Replies: 75
Views: 7,154
Posted By kijinSeija
Thanks for your answer. By the way, do you...

Thanks for your answer.

By the way, do you know the condition for example 6*p+1 or 10*p+1 divides 2^p-1 ?

I know the condition for 2*p+1 but I have no idea for these two for example.
Forum: Dobri 2022-04-18, 16:15
Replies: 75
Views: 7,154
Posted By kijinSeija
4p+1 never divides 2^p-1 right ? I can't find the...

4p+1 never divides 2^p-1 right ? I can't find the sequences in OEIS
Forum: Math 2021-12-11, 16:40
Replies: 22
Views: 4,143
Posted By kijinSeija
Ok thank you for that information. I only...

Ok thank you for that information.

I only know ECCP in your list :confused:
Forum: Math 2021-12-11, 16:12
Replies: 22
Views: 4,143
Posted By kijinSeija
Sure sorry I will edit. I don't know if...

Sure sorry I will edit.

I don't know if "probable primality test" exists by the way :)

Nevermind it exists.

So when a prime is found by some primality test with no proof for the primality...
Showing results 1 to 25 of 41

 
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