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Forum: Computer Science & Computational Number Theory

2021-07-11, 13:26

Replies: 5

2-symbol, 5-state Turing machine

Views: 3,121

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

Possible proof of Reix' conjecture (Wagstaff primes, plus some issues)

Views: 8,580

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

Factoring as the problem of quadratic minimization

Views: 832

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

Factoring as the problem of quadratic minimization

Views: 832

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

Possible proof of Reix' conjecture (Wagstaff primes, plus some issues)

Views: 8,580

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...

Forum: Computer Science & Computational Number Theory

2019-10-24, 16:12

Replies: 6

Leading numbers of tetration

Views: 5,746

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...

Forum: Computer Science & Computational Number Theory

2019-02-10, 04:04

Replies: 5

2-symbol, 5-state Turing machine

Views: 3,121

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...

Forum: Computer Science & Computational Number Theory

2019-02-09, 08:24

Replies: 5

2-symbol, 5-state Turing machine

Views: 3,121

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

Forum: Computer Science & Computational Number Theory

2019-01-25, 18:41

Replies: 6

Leading numbers of tetration

Views: 5,746

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?".

Forum: Computer Science & Computational Number Theory

2019-01-25, 11:25

Replies: 6

Leading numbers of tetration

Views: 5,746

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

Why integer factorization is in P/FP?

Views: 2,150

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

Why integer factorization is in P/FP?

Views: 2,150

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

Where is a new fast algorithm of factorization?

Views: 2,252

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

Where is a new fast algorithm of factorization?

Views: 2,252

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

Where is a new fast algorithm of factorization?

Views: 2,252

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...

Forum: Other Mathematical Topics

2019-01-20, 17:12

Replies: 1

New conjecture about Mersenne primes

Views: 2,737

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

Forum: Other Mathematical Topics

2019-01-20, 15:47

Replies: 1

New conjecture about Mersenne primes

Views: 2,737

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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