If $n\ge 3$ is an integer :
Can $N=n!-1$ or $N=n!+1$ , except $5!+1$ , satisfy $3^{N-1}\equiv 1\mod N$ , but nevertheless be composite , in other words can $n!-1$ or $n!+1$ , except $121$ , be a weak 3-pseudo-fermat prime ?
For $3\le n\le 1\ 000$ , neither of the numbers has this property with the mentioned exception $5!+1=121=11^2$.