Mark Petry wrote, surely with tongue in cheek:
"41t rings are hard to find and very cool! Other than a "little bit lower" ratio, I have it on good authority (ahem) that they were used frequently as synchronizing rings on tandems, where a prime numbered ring is purported to have better wear characteristics.
Whoa! Mark, I'm going to take the bait. In a series of miserable, unplanned, empirical experiments involving an on-topic Schwinn Town-and-Country and transfer cogs ordered from R.E.W. Reynolds in England, I was forced to confront the fact that tandem eccentric bottom brackets can only take up a limited amount of chain. The exact length of the "boob tube" (bottom bracket connector tube) on that bike was such that it absolutely required even numbers of teeth on the transfer cogs. With a slightly shorter boob tube, I suspect that only odd tooth numbers would work. Evens worked fine on the T&C, and allowed use of the eccentric to take up slack as the chain wore. Odd tooth rings could only be set up as too-loose, or won't-stretch-to-fit. Of course, I am using an artificial constraint, in assuming that both transfer cogs have the same number of teeth, so pedaling doesn't go out of phase and then back in phases and all that stuff...
Your mileage may vary more than the tooth count :-)
harvey sachs
mcLean va