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 Showing results 1 to 13 of 13 Search took 0.01 seconds. 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 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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