I pushed the direct search for Bell/Wilson pseudoprimes up to n <= 4096, taking 4 hours --- there are none in this range. On 7/22/07, Fred lunnon <fred.lunnon@gmail.com> wrote:
Note that there may be a smaller one --- my program searched in order of smallest prime factor p, and found only that there are no more pseudoprimes for p < 60.
An over-simplification: this cofactor search program actually enumerates by quotient n/q of largest prime factor q, finding all possible such q. Anyhow, a 10 hour run took n/q up to 73, finding just one more pseudoprime: n = 69 * 16218646893090134590535390526854205539989357 (46 digits) Doesn't look as though there are too many of these things around! These searches employ a Dobinski-based Bell(n) function, also a recurrence- based Bell(n) mod m, which is faster for large n and small m. Maple and Magma implementations available on request [you interested, JJA?] Fred Lunnon