### References & Citations

# Mathematics > Logic

# Title: Is the twin prime conjecture independent of Peano Arithmetic?

(Submitted on 16 Oct 2021 (v1), last revised 2 Nov 2021 (this version, v3))

Abstract: We show that there is an arithmetical formula F such that ZF proves that F is independent of PA and yet, unlike other arithmetical independent statements, the truth value of F cannot at present be established in ZF or in any other trusted metatheory. In fact we can choose an example of such a formula F such that ZF proves that F is equivalent to the twin prime conjecture.

## Submission history

From: Antongiulio Fornasiero [view email]**[v1]**Sat, 16 Oct 2021 18:51:18 GMT (5kb)

**[v2]**Tue, 19 Oct 2021 16:18:23 GMT (5kb)

**[v3]**Tue, 2 Nov 2021 08:06:21 GMT (6kb)

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