Problem 472

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Statement. Given some initial finite sequence of primes $q_1<\cdots<q_m$ extend it so that $q_{n+1}$ is the smallest prime of the form $q_n+q_i-1$ for $n\geq m$. Is there an initial starting sequence so that the resulting sequence is infinite?

Status. Open.

Source. erdosproblems.com/472, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #472, https://www.erdosproblems.com/472.

Formalization. None recorded.

Progress

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Known Results

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