{"schema":"vela.problem-packet.v0.1","problem":979,"statement":"Let $k\\geq 2$, and let $f_k(n)$ count the number of solutions to\\[n=p_1^k+\\cdots+p_k^k,\\]where the $p_i$ are prime numbers. Is it true that $\\limsup f_k(n)=\\infty$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A385316","name":"Smallest number that is the sum of 3 cubes of primes in exactly n different ways.","terms":"24,185527,8627527,999979163,10588881419","url":"https://oeis.org/A385316"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}