Counting Prime Numbers

Some engineering folks at Google came up with a "Treasure Hunt" about a month ago, consisting of four puzzles. One new puzzle was released each week. There was probably a prize involved at some point. As far as I could tell, the purpose of the game was twofold: (1) to show off Google's new app engine; and (2) probably as a recruiting tool. Reason (2) is suspected due to the nature of the puzzles released the second and third weeks.

I particularly liked the last puzzle. It looks like the following:

Find the smallest number that can be expressed as

the sum of 3 consecutive prime numbers,
the sum of 81 consecutive prime numbers,
the sum of 561 consecutive prime numbers,
the sum of 745 consecutive prime numbers,
and is itself a prime number.

For example, 41 is the smallest prime number that can be expressed as
the sum of 3 consecutive primes (11 + 13 + 17 = 41) and
the sum of 6 consecutive primes (2 + 3 + 5 + 7 + 11 + 13 = 41).

In this case, the answer is 6929191. However, the parameters of the puzzle are different every time you go to the site. It's always to find a prime number that can be expressed as the sum of A, B, C, and D prime numbers, but A, B, C, and D vary.