The reciprocal sum of the prime-prefix-free numbers (https://oeis.org/A287117) converges to a number less than 5*10^14, conditional on the Riemann Hypothesis.

This Lean-verified proof answers a question I posed 10 years ago: https://math.stackexchange.com/questions/2288648/does-the-su...

An equivalent version: if we start with 1 and then output a stream of random bits, reading the number as a big-endian binary number at each step (so each time a bit arrives, the number is multiplied by 2 and 1 is either added or not), the expected time until the number is an odd prime is finite.