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 Showing results 1 to 25 of 30 Search took 0.01 seconds. Search: Posts Made By: kijinSeija
 Forum: Math 2022-06-12, 20:37 Replies: 3 Views: 1,856 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: 322 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). ...
 2022-04-30, 21:23 Replies: 6 Views: 437 Posted By kijinSeija thanks for your help and for the address :grin: thanks for your help and for the address :grin:
 2022-04-30, 19:39 Replies: 6 Views: 437 Posted By kijinSeija (((30809^30809)%30809#)/30809) is 3-PRP! ... (((30809^30809)%30809#)/30809) is 3-PRP! (((42017^42017)%42017#)/42017) is 3-PRP!
 2022-04-30, 16:12 Replies: 6 Views: 437 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: 29 Views: 3,238 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: 29 Views: 3,238 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: 29 Views: 3,238 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: 29 Views: 3,238 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: 29 Views: 3,238 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: 29 Views: 3,238 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: 29 Views: 3,238 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: 3,471 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: 3,471 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: 3,471 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: 3,471 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: 639 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: 639 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: 639 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: 639 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: 639 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: 639 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: 3,839 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: 3,839 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: 3,839 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...
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