Hou and Zeng's prime–Fibonacci–Catalan representation conjecture

Let $F_n$ denote the Fibonacci numbers, and let

$$C_n=\frac{1}{n+1}\binom{2n}{n}$$

be the $n$th Catalan number. A Fibonacci number is positive when it is positive as an integer. Hou and Zeng's prime–Fibonacci–Catalan conjecture. Every integer $n>4$ can be written as

$$n=p+F_s+C_t,$$

where $p$ is an odd prime, $F_s$ is a positive Fibonacci number, and $C_t$ is a Catalan number. The source attributes the conjecture to Qing-Hu Hou and Jiang Zeng and reports verification up to $3\times10^{13}$; it remains open.