New Mersenne Prime discovered (probably)

lol, like the government doesn't have 3 more Mersennes they keep secret so they can verify potential First Contact situations

the idea of a deep-nation-state-cold-war psyop campaign bluffing and escalating math proofs is so goddamn hilarious, apt, and ironic it would be almost better than the mistake of pissing off the Aliens by offending them with math homework.

"Shizuo Kakutani joked that the problem [Collatz conjecture] was a Cold War invention of the Russians meant to slow the progress of mathematics in the West."

They're much easier to verify than to find. Just ask for the next one hundred unknown primes and check the response.

This still suffers from the MitM / Two Generals Problem, and is existentially problematic if they also demand the simple, reasonable sum of the first BB(17) numbers modulo Grahams number, within 14 business local parsec-years.

Their spam filter may be an annoying ping acknowledgement, a directed gamma ray beam from soft gamma repeater, just to irradiate their own hoax-doers suspects.