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 = 73
(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.