Consecutive primes with only odd digits

In response to a problem posed by Mark Underwood on the "Prime Numbers" Yahoo!Group.

3,5,7,11,13,17,19 are the first set of seven consecutive primes with only odd digits, so a(7)=3.

Here's a table of the smallest starting points for sequences of increasing length runs of primes with only odd digits:

Distribution of lengths:

length	count
7	33984
8	5605
9	1054
10	197
11	43
12	9
13	1

Note: Jens has found 5 length 13 runs in his magnificent hunt up to 10^14 (I only went to ~3.9e13).

Anyone with any ideas about the asymptotics? Anyone with a 14?

Last updated 2003/07/10