How many primes, written in usual base 10, have digits that are alternating 1s and 0s, beginning and ending with one?

For example (not necessarily prime):
1, 101, 10101, ...

If there are a multiple of 3 ones, it will be divisible by 3, since 10101 = 3*3367. So 10101...01 is not prime if the number of ones is:

even and greater than 2
a multiple of 3

Posted by Brian Wainscott on 2004-02-18 14:25:17