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Claim. P. Pollack, Some arithmetic properties of the sum of proper divisors and the sum of prime divisors, Illinois J. Math. 58 (2014), no. 1, 125--147, Theorem 1.11: for all $x\ge2$, the number of $n\le x$ for which $s(n)$ is prime is $O(x/\log x)$ (card). So the preimage under $s$ of the primes, a set of density zero, has density zero, which is the assertion of Problem 955 for that set. The issue is dated Spring 2014; the publisher records online publication on 1 April 2015, so this page carries that date.

Covers. The instance $A$ = the primes; the general assertion stays open.

Depends on. No page of this wiki.

Acceptance. Refereed: Illinois Journal of Mathematics. The site's commentary credits the result, but the site labels the problem OPEN, so no curator acceptance is listed.