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]

Transdenumerability of the reals

[white paper]

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We show that the real numbers are transdenumerable by setting a one to one map with the set of the transfinite ordinals introduced by Cantor.

https://doi.org/10.31219/osf.io/fu7bx

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 156, 2020 [GD]

A unidimensional windmill in the plane with varying pivot points

[white paper]

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We show that we can choose a point in the plane such that the resulting windmill process with varying pivot uses each point of the plane infinitely many times.

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

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 148, 2020 [FT]

Generating finitely many circles from one circle using Banach-Tarski decomposition paradox

[microreview]

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We prove the Banach-Tarski decomposition paradox applied to a circle.

https://doi.org/10.31219/osf.io/mh5gx

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 142, 2020 [FN]

A subgroup has equally many left and right cosets

[microreview]

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We prove that a subgroup has the same number of left and right cosets.

https://doi.org/10.31219/osf.io/t4snh

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 137, 2020 [FH]