With the hysteria surrounding the Powerball jackpot, I'm sure a lot of you have been thinking about the tiny odds of a lottery in which you have to match five or six numbers out of a small set (like 1 to 80).
What if there was a lottery in which a single even number between, say, $10^{10}$ and $10^{20}$ is chosen? But you don't have to match that number, you have to match more prime factors below $10^5$ than any other player. And you only get to choose five or six such primes. Let's say that for a particular drawing no player matches five primes but a few players match four primes. The player matching the larger primes would win the jackpot.
Such a lottery would be quite difficult for the average gambler. But for you who have studied prime factorization: what would be some winning strategies?