Primes in Different Bases
Pyth, 25 bytes

sfTm&gt;1PiFdC,.u-N`tYKrT1zK




                       z   get input as a string
            .u      rT1    cumulative reduce over [10,9,...,2]
              -N`tY        remove one minus the number (10,9,...) from the input
          C,       K    K  pair each step along the chain with corresponding base
   m                       map over [["987654321", 10],...]:
       iFd                   apply the base-conversion (splat over i)
      P                      prime factorization, smallest to largest
    &gt;1                       take [the last element], or [] if empty (1 or 0)
 fT                        remove the []s from 0s or 1s
s                          join the one-element arrays together


Try it here.