Prime anagrams

[hv at crypt.org]

zak seidov <zakseidov at yahoo.com> wrote:
:Take five (decimal) digit prime number. 
:Check all anagrams for primarity, 
:and count the prime numbers.
:
:E.g. there are 39 primes with (decimal) digits
:1,3,7,8,9:
:13789,13879,17389,17839,18379,18397,18793,18973,19387,37189,38197,38791,38917,38971,71389,71983,73189,73819,78139,78193,79813,81937,81973,83719,83791,87931,89137,89317,89371,91387,91837,91873,93187,93871,97381,97813,98317,98713,98731
:(not(?) in OEIS).
:
:The number 39 is maximal(?) for 5d prime anagrams.
:
:What about other cases?
:Thanks, Zak

Here's some numbers I calculated:

 n a(n)    b(n) c(n)    d(n)
============================
 1    1       2    1       2
 2    2      13    2      13
 3    4     149    4      17
 4   11    1237   11    1237
 5   39   13789   39   13789
 6  148  123479  160   13789
 7  731 1235789  738  123479

n = number of digits; a(n) = maximal number of permutations that are prime;
b(n) = smallest prime example of a(n); c(n) = a(n) but allowing leading zero
digits; d(n) = smallest prime example of c(n).

I got these using a simple, not very extensible approach, but I'm sure
someone with a decent list of primes to hand could extend them readily.
(I'm sure someone pointed at a large downloadable list recently, but I
didn't save the reference.)

I feel that analysis of the asymptotic behaviour of a(n) and c(n) could be
interesting: my initial reaction was that c(n) would come to dominate a(n),
but it may not be so clear cut.

Hugo V.