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March 27, 2026Open Access

Infinitely Many Sophie Germain Primes

Key Points

The aim is to prove that there are infinitely many Sophie Germain primes, which are primes p such that 2p+1 is also prime.
Mathematical proof techniques
Analysis of prime properties
Number theoretic exploration
The proof confirms the existence of infinitely many Sophie Germain primes.
It establishes the relationship between primes and their related forms.

Abstract

Preprint v1 — A proof that there are infinitely many primes p such that 2p+1 is also prime. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings. Author: Joseph Keen Affiliation: Phoenix Quantum Labs LLC

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Cite this study

Joseph R. Keen (Wed,) studied this question.

www.synapsesocial.com/papers/69c61f5615a0a509bde17ebe — DOI: https://doi.org/10.5281/zenodo.19216446

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Joseph R. Keen

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