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 Showing results 1 to 17 of 17 Search took 0.01 seconds. Search: Posts Made By: tetramur
 2021-07-11, 13:26 Replies: 5 Views: 2,834 Posted By tetramur Actually, several months ago I got precise... Actually, several months ago I got precise decimal expansion of both numbers via Haskell "hindu" program. I write them below (broken into lines 50 digits each): Σ(2,5) ≥ ...
 Forum: Wagstaff PRP Search 2021-07-11, 09:31 Replies: 5 Views: 7,905 Posted By tetramur Thanks for your feedback. Anyway, it'll be... Thanks for your feedback. Anyway, it'll be interesting to prove Conjecture 1. Maybe one day I'll post the proof here.
 Forum: Factoring 2021-07-01, 06:11 Replies: 3 Views: 702 Posted By tetramur Yes, exactly. I intended solution to be integers.... Yes, exactly. I intended solution to be integers. Also, I checked that integer optimization problems are NP-complete in general, but I don't know if this particular problem is NP-complete.
 Forum: Factoring 2021-06-30, 18:52 Replies: 3 Views: 702 Posted By tetramur Factoring as the problem of quadratic minimization The factoring is trivially equivalent to following minimization problem: Minimize x1*x2 with these conditions: x1*x2 >= N 2 <= x1 <= N-1 2 <= x2 <= N-1 x1 <= x2 Question: is it possible to get...
 Forum: Wagstaff PRP Search 2020-09-10, 16:29 Replies: 5 Views: 7,905 Posted By tetramur Possible proof of Reix' conjecture (Wagstaff primes, plus some issues) I claim to have proved the Reix' conjecture (2007), part "if": Theorem 1.1. Let p > 3 prime and for the sequence S0 = 3/2, Sk+1 = Sk^2 − 2 it is true that S(p-1) − S0 is divisible by W(p), then...
 2019-10-24, 16:12 Replies: 6 Views: 5,214 Posted By tetramur I'm currently trying to evaluate the fractional... I'm currently trying to evaluate the fractional part of the logarithm of tetration using repeated squaring - but I want to evaluate this number (between 0 and 1) directly, 'cause this becomes quickly...
 2019-02-10, 04:04 Replies: 5 Views: 2,834 Posted By tetramur Of course! Sigma (2,5) - the highest number of... Of course! Sigma (2,5) - the highest number of non-zero symbols that Turing machine with 2 symbols and 5 states can print. S (2,5) - the same definition, but in this time we have the highest...
 2019-02-09, 08:24 Replies: 5 Views: 2,834 Posted By tetramur 2-symbol, 5-state Turing machine Does anyone have the current records for Sigma (2,5) & S (2,5)? I want to obtain full decimal expansion for they... At the moment we have: Sigma (2,5) > 1.7 * 10^352 S (2,5) > 1.9 * 10^704
 2019-01-25, 18:41 Replies: 6 Views: 5,214 Posted By tetramur No, it is unknown by now. But question is: "Do it... No, it is unknown by now. But question is: "Do it exist?".
 2019-01-25, 11:25 Replies: 6 Views: 5,214 Posted By tetramur Leading numbers of tetration I would like to solve this problem. Question: Can the algorithm for finding the leading digits of some tetration with time complexity of iterational logarithm (or, ideally, the constant time...
 Forum: Factoring 2019-01-23, 15:10 Replies: 4 Views: 1,947 Posted By tetramur What I already have said. There can not be... What I already have said. There can not be elementary proof of P = NP. If it was true, why scientists searched for proofs since 1970s and could not find?
 Forum: Factoring 2019-01-23, 11:47 Replies: 4 Views: 1,947 Posted By tetramur Why integer factorization is in P/FP? http://www.optimization-online.org/DB_FILE/2012/08/3591.pdf https://www.researchgate.net/post/Can_AKS_prime_number_test_be_modified_to_factorize_in_polynomial_time I have some reasons to verify it...
 Forum: Factoring 2019-01-22, 07:36 Replies: 8 Views: 1,959 Posted By tetramur Can method used by Joux et al. be extended with... Can method used by Joux et al. be extended with keeping time complexity the same? If yes, how can it be done?
 Forum: Factoring 2019-01-22, 05:40 Replies: 8 Views: 1,959 Posted By tetramur No. An algorithm for DL implies algorithm for IF... No. An algorithm for DL implies algorithm for IF and vice versa. Look! Elliptic curves QS (only IF?) NFS IC (only DL?) IF and DL are related....
 Forum: Factoring 2019-01-21, 11:21 Replies: 8 Views: 1,959 Posted By tetramur Where is a new fast algorithm of factorization? A. Joux created in 2013 a new algorithm (index calculus, JIC) for finding a discrete logarithm with time complexity of LQ (1/4, c) for c > 0. Can we find an algorithm for integer factorization with...
 2019-01-20, 17:12 Replies: 1 Views: 2,557 Posted By tetramur Easy - disproven. Counterexample: Take r =... Easy - disproven. Counterexample: Take r = 1279 (prime), p = 557, q = 1117. ((M_1279)^557-557) mod 1117 = 713 1117 mod 713 = 404, not +/-1 713 is not square M_1279 mod 557 = 269
 2019-01-20, 15:47 Replies: 1 Views: 2,557 Posted By tetramur New conjecture about Mersenne primes William Bouris claimed in his mad proofs, that: "if p= 4*k+1, and q= 2*p+3 are both prime, then if [(M_r)^p-p] mod q == N, and q mod N == +/-1, then (M_r), the base, is prime. also, if (M_r) mod p =...
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