How to calculate the cost of factoring a large integer? I would like to know how much it would cost to factor a large integer. The cost can be given computer operations, time to process it or even monetary value. I know there are people that factored 200 bit RSA keys, but Wikipedia doesn't say how long it would take in modern CPUs.

-- Background --

I am designing a virtual roulette game where the ball is spun (the number is chosen) before the player bets. As a proof of that but I show the player the product of two primes, one of them is used as the random number seed.

I would like to know what is the minimum suitable size for this number such as the cost of factoring it will be greater than the maximum prize I offer.
To turn the question around, one could equivalently ask: "How large must my prime be in order to be secure until year X against the resource plausibly available to a potent (e.g. government-funded) attacker?" This question is being regularly reassessed in various studies yielding recommended key lengths for crypto systems. A regularly updated web page summarizing these reports can be found here.