SIMON-MARAIS 2024 A4

Paper A

Define a sequence by $s_0 = 1$ and for $d \geq 1$ , $s_d = s_{d-1} + X_d$ , where $X_d$ is chosen uniformly at random from the set $\{1, 2, \ldots, d\}$ .

What is the probability that the sequence $s_0, s_1, s_2, \ldots$ contains infinitely many primes?

Official text Simon Marais Mathematics Competition 2024 official paper, page 2. Quoted with source.

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