[math-fun] Chernick numbers

"J. Chernick[6] <http://en.wikipedia.org/wiki/Carmichael_number#cite_note-Chernick1939-6> proved a theorem in 1939 which can be used to construct a subset <http://en.wikipedia.org/wiki/Subset> of Carmichael numbers. The number [image: (6k + 1)(12k + 1)(18k + 1)] is a Carmichael number if its three factors are all prime." (I used to think these were the only Carmichael numbers.) Isn't it fairly immediate that this can be simplified to p*(2p-1)*(3p-2), p>3, all three factors prime, since 2p-1 can't be prime when mod(p,6)=5? --rwg