[science_man_88]

Originally Posted by carpetpool

So just looking on the conditions mod 3 we have:

a = 1
b = 2
c = 1

a = 0
b = 0
c = 1

I also thought about another exception: n may also define properties of the cyclotomic field K if and only if each prime power p^k dividing n is either 0 or 1 mod n.

So in this sense, factors such as 2^2, 5^2, 11^2, 17^2, 23^2, 29^2..., etc. would be allowed, but I don't know weather this would make problem harder.

well with one more command combination in PARI/gp you'll find that 386 of those 400 are considered irreducible.