24 May
2004
24 May
'04
4:02 p.m.
factorization of Q(N) = N^2+N+1 ... there appears to be an unusually high frequency of Q(N)'s being prime. And also when Q(N) is composite, it appears as though there tend to be unusually few factors (and unusually large ones).
Is there a theory that would confirm these suspicions?
I might know a little bit about that... Q is the third cyclotomic polynomial, a factor of N^3-1, and Q(N) can't be divisible by a 6k-1 prime. Since there are fewer prime factors to choose from, you get fewer factors, and more primes. See also http://www.asahi-net.or.jp/~KC2H-MSM/cn -- Don Reble djr@nk.ca