The Complexity of Mathematics

Frank Vega

doi:10.20944/preprints202002.0379.v4

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preprints.org > computer science and mathematics > computational mathematics > doi: 10.20944/preprints202002.0379.v4

Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

The Complexity of Mathematics

Frank Vega

Version 1 : Received: 24 February 2020 / Approved: 25 February 2020 / Online: 25 February 2020 (12:21:49 CET)
Version 2 : Received: 27 February 2020 / Approved: 27 February 2020 / Online: 27 February 2020 (10:49:49 CET)
Version 3 : Received: 10 March 2020 / Approved: 11 March 2020 / Online: 11 March 2020 (16:04:28 CET)
Version 4 : Received: 31 March 2020 / Approved: 2 April 2020 / Online: 2 April 2020 (18:25:32 CEST)
Version 5 : Received: 20 April 2020 / Approved: 22 April 2020 / Online: 22 April 2020 (09:48:30 CEST)
Version 6 : Received: 3 June 2020 / Approved: 4 June 2020 / Online: 4 June 2020 (13:22:40 CEST)
Version 7 : Received: 6 June 2020 / Approved: 8 June 2020 / Online: 8 June 2020 (10:31:19 CEST)
Version 8 : Received: 2 July 2021 / Approved: 6 July 2021 / Online: 6 July 2021 (12:38:05 CEST)
Version 9 : Received: 14 October 2021 / Approved: 14 October 2021 / Online: 14 October 2021 (14:15:38 CEST)

How to cite: Vega, F. The Complexity of Mathematics. Preprints 2020, 2020020379. https://doi.org/10.20944/preprints202002.0379.v4 Vega, F. The Complexity of Mathematics. Preprints 2020, 2020020379. https://doi.org/10.20944/preprints202002.0379.v4

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MDPI and ACS Style

Vega, F. The Complexity of Mathematics. Preprints 2020, 2020020379. https://doi.org/10.20944/preprints202002.0379.v4

APA Style

Vega, F. (2020). The Complexity of Mathematics. Preprints. https://doi.org/10.20944/preprints202002.0379.v4

Chicago/Turabian Style

Vega, F. 2020 "The Complexity of Mathematics" Preprints. https://doi.org/10.20944/preprints202002.0379.v4

Abstract

The strong Goldbach's conjecture states that every even integer greater than 2 can be written as the sum of two primes. The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A principal complexity class is NSPACE(S(n)) for some S(n). We show if the weak Goldbach's conjecture is true, then the problem PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n). However, if this happens, then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples. In addition, if this happens, then the Twin prime conjecture is true. Moreover, if this happens, then the Beal's conjecture is true. Furthermore, if this happens, then the Riemann hypothesis is true. Since the weak Goldbach's conjecture was proven, then this will certainly happen.

Keywords

complexity classes; regular languages; reduction; number theory; conjecture; primes

Subject

Computer Science and Mathematics, Computational Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 2 April 2020
Commenter: Frank Vega
Commenter's Conflict of Interests: Author

Comment: The title, abstract and the content of the paper were changed. My intention is not to withdraw it, but to submit this new version instead. If you receive a notification of withdrawal, then I confirm it was not me. Thanks in advance.

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