Is there a proof for the (non)existence of a formula for prime numbers?

[question]

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We discuss about whether it is possible or not to prove or disprove the existence of a formula for the prime numbers.

https://doi.org/10.31219/osf.io/sb7td

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 167, 2020 [GO]

On the arithmetic of automated theorem proving

[white paper]

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We propose a model to assign prime numbers to axioms and theorems, then by comparing equivalent numbers, it results in new equivalent theorems.

https://doi.org/10.31219/osf.io/wbf85

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 132, 2020 [FC]

Logical Loop

[microresearch]

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We discuss the dubbed term “logical loop” and it’s implication regarding provability in undecidable theorems.

https://doi.org/10.31219/osf.io/c5ezm

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 123, 2020 [ET]

Using prime numbers for automatic theorem proving

[original idea]

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We apply an analogous setting from Gödel’s numbering system to automatic theorem proving.

https://doi.org/10.31219/osf.io/g7usc

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 119, 2020 [EP]

Non-classical logic and undecidability

[conjecture]

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We elaborate a conjecture by applying the definition of Non-Axiomatic System [1] in Non-Classical Logic.

https://doi.org/10.31219/osf.io/h4f7p

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 112, 2020 [EI]

Mathematics beyond axioms

[microresearch]

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We consider that if there is a Non-Axiomatic System, then by introducing the axiom of mathematical proof, the undecidable theorems are not in any Axiomatic System.

https://doi.org/10.31219/osf.io/adrjq

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 46, 2019 [BT]

Gödel’s incompleteness theorem in a nutshell

[microreview]

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We present a microversion of Gödel’s theorem.

https://doi.org/10.31219/osf.io/gphsk

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 1, Article 45, 2019 [BS]