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Claim. Equation (3) of P. Erdős, Számelméleti megjegyzések I, Mat. Lapok 12 (1961), 10–17 (card):

$$\sum_{p<x}n_2(p)=(1+o(1))\frac{x}{\log x}\sum_{k\ge1}\frac{p_k}{2^k},$$

where $n_2(p)$ is the least quadratic nonresidue modulo $p$ and $p_1<p_2<\cdots$ are the primes. It answers a question of Mirsky and is proved with Linnik's large sieve together with Brun's sieve and the prime number theorem for progressions.

Covers. The case $k=2$ of the Statement of Problem 980.

Acceptance. A refereed journal publication (refereed). The curator's PROVED label credits Elliott for the general case, and $k=2$ is not a part under the parts rule, so the label is not curator credit for this page.

Depends on. No page of this wiki.