Nagabinary evil and odious primes are primes in A268272 and A268273 correspondingly.

They are 2,5,7,13,17,19,31,37,61,67,73,79,...

and 3,11,23,29,41,43,47,53,59,71,83,89,...

In contrast to the analogous sequences for odious and evil primes (A027697, A027699), which, as we conjecture, consists of only primes 3,7,29 (see also our 2007-conjecture in A027697, A027699), here we conjecture that the sequence is infinite.