# [FRACTRAN](https://en.wikipedia.org/wiki/FRACTRAN), 144 bytes

    29/14 222/377 59/26 247/59 329/57 19/47 2/19 11/29 403/407 217/33 11/31 2/11 1/37 1/2 23/9 43/69 23/43 1/23 425/41 4823/85 17/53 41/25 2/119 1/5

This took me way longer than expected - special casing `1` was pretty annoying. Takes `5^n` as input and outputs `3^0 = 1` (falsy) if composite, or `3^1 = 7` (truthy) if prime.

The approach is similar to Conway's prime generator, performing a divmod on descending divisors. This isn't as compact though, so there's still much to golf.