1021

This number is a prime.

Note that in the matrix product:

[ 1 0 ] [ 2 3 ]   [ 2 3 ]
                =
[ 2 1 ] [ 1 1 ]   [ 5 7 ]

1021 is prime, 2311 is prime, 2, 3, 5 and 7 are the first four primes (and incidentally, 2357 is prime). This is the only pair of 2-by-2 matrices with this property. [Hartley]