Hold onto your hats, folks -- I have stumbled across something VERY interesting. In case it's original, let's call it the Tovish Conjecture. Here goes (dB2n stands for the denominator of the even Bernoulli numbers (the odds are all zero):

If n is a prime number, then dB2p largest factor is p!

If n is not a prime, the dB2n factors are all smaller than n.

This provides a test for whether a number is a prime: derive dB2n, if it divides by n without a remainder, then n is a prime.

I have checked this out to n=101. Does it always hold true? Even if it does, is this an efficient or inefficient way to determine primes?

Anyone know??