Ask Dr. SETI ®

If the 6 represents the wavelength of the f-hydrogen = 1420.4 MHz frequency emitted by hydrogen, then the prime number slots might correspond to sidebands at f-hydrogen plus or minus f-hydrogen/6. Since 1420.4/6 = 236.7 MHz, one might want to look at:

1420.4 + 236.7 = 1657.1 MHz and
1420.4 - 236.7 = 1183.7 MHz

Roger C., via email

The Doctor Responds:
There are a number of different algorithms which have been used to seek "magic SETI frequencies," Roger. Only those which do not derive from any geocentric concept or system of measure might be valid. Any mathematical series (including the one you cite) is fine for deriving likely numbers, but what do we do with those numbers once we have them, that doesn't involve concepts unique to Earth? That's the challenge!

A multiple of a basic emission line (like hydrogen) is fine, because hydrogen emission is universal, and looks the same to all observers in the Universe, no matter how we tally its units (or no matter how many fingers ETI counts on). We must take care, however, not to assign significance to a certain (magic) number of MegaHertz, for example, because Mega is merely a result of counting in decimal, and Hertz is cycles per second, a very arbitrary measure of time used on Earth.

All that said, I should point out that there's a move in the SETI community away from searching on or around "magic frequencies," in favor of developing ultra-broadband receivers that can search at all frequencies simultaneously. If you're looking across the entire electromagnetic spectrum (a tall order to be sure), then there's little chance you will have guessed wrong.

As an interesting aside, your algorithm for determining primes is somewhat reminiscent of that for a special case, the Mersenne Primes. These are numbers which fit the form:

n = 2^P - 1