how many integers between 0 and 1560...

Great question, euro - here's how I'd look at this one:

1) Determine how many prime digits there are (2, 3, 5, 7 --> there are 4 of them)

2) Determine how many numbers meet the requirements per hundred: There are 4 potential tens digits and 4 potential units digits so there are 16 potential numbers (4x4) per hundreds digit. (e.g. 22, 122, 222, 322....)

3) So there are 16 possibilities per fresh set of 100, and there are 15 hundreds/hundreds-and-thousands digits that have "full sets" (0-14).

4) The 16th set of 100 is truncated at 60 (1500 - 1560), so we need to account for the fact that 7 as a tens digit doesn't work on that one. Therefore there are 3 potential tens digits and 4 potential units digits, so there are 3*4 = 12 potential numbers in that set.

Therefore, our number is going to be 15*16 + 12 = 252.