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Reciprocal sum of prime-prefix-free numbers shown to converge

Original: The reciprocal sum of the prime-prefix-free numbers converges [pdf]

A new paper proves that the sum of reciprocals of the prime-prefix-free numbers — integers that share no common prefix, digit by digit, with a prime — converges to a finite value. The result settles a question about a set whose sum of reciprocals was not obviously finite or infinite. Readers of a mathematics-focused discussion site are engaging with the short proof and debating the counting argument behind it.

Why now: A newly published proof resolves a number theory question, drawing attention from math enthusiasts.

prime-prefix-free numbersnumber theory

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