Erdős problem 427 · problems.science

Erdős Problem 427: is it true that, for every $n$ and $d$ , there exists $k$ such that $d \mid p_{n + 1} + \cdots + p_{n + k},$ where $p_r$ denotes the $r$ th prime?

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FormalConjectures/ErdosProblems/

427.lean

Retained formal statement3 of 3

Shiu's theorem: for any $k \geq 1$ and $(a, q) = 1$ there exist infinitely many $k$ -tuples of consecutive primes $p_m, \dots, p_{m + k - 1}$ all of which are congruent to $a$ modulo $q$ .

[Sh00] Shiu, D. K. L., _Strings of congruent primes_. J. London Math. Soc. (2) (2000), 359-373.

FormalConjectures/ErdosProblems/427.leanErdos427.erdos_427.variants.shiu1 lineExact file

1Erdos427.ShiuTheorem

SolvedStatement only, no proof

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