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Search: Posts Made By: kijinSeija
Forum: Math 2022-05-13, 20:32
Replies: 0
Views: 230
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: 277
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: 277
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: 277
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: 27
Views: 1,876
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: 27
Views: 1,876
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: 27
Views: 1,876
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: 27
Views: 1,876
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: 27
Views: 1,876
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: 27
Views: 1,876
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: 27
Views: 1,876
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: 3,156
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: 3,156
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...
Forum: Math 2021-12-11, 15:58
Replies: 22
Views: 3,156
Posted By kijinSeija
I don't know if it fits with this topic but maybe...

I don't know if it fits with this topic but maybe I found a probable primality test for the number of the form (3^p-1)/2. I don't if it's new at all :


Let N = (3^p−1)/2 when p is a prime number...
Forum: Math 2021-12-10, 10:08
Replies: 22
Views: 3,156
Posted By kijinSeija
I tried some new seeds and -9/8 works for...

I tried some new seeds and -9/8 works for Wagstaff numbers. At least until 1000
Forum: Miscellaneous Math 2021-12-08, 13:26
Replies: 10
Views: 583
Posted By kijinSeija
I get a false positive with n = 4 for 3*2^n+1. So...

I get a false positive with n = 4 for 3*2^n+1. So it doesn't works for Pq at least when n < 5.
Forum: Miscellaneous Math 2021-12-07, 17:50
Replies: 10
Views: 583
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: 10
Views: 583
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: 10
Views: 583
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: 10
Views: 583
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: 10
Views: 583
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: 12
Views: 3,545
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: 12
Views: 3,545
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: 12
Views: 3,545
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: 12
Views: 3,545
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...
Showing results 1 to 25 of 29

 
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