or produce guaranteed unique cryptographic tokens that are impossible to fake, rework, deteriorate or replace, for the purpose of economical utility and reduced resources waste.
This one has my vote.
1 BTC : 20 Bucks (atm)
1 BTC : 5 Bucks (Some time in the future)
Cure for AIDS : Priceless
You have the values of BTC wrongly, in the future 1 BTC will be worth more than it is today. AIDS is still treatable (you can live 35 years more with anti-viral medication, you can have children that are AIDS free with proper care and you can prevent AIDS by using a 0.5$ prophylactic). Scientists are already working on some vaccines at the moment and the answer is not found in computation.
But if you think you want to help the world while receiving the costs of doing so, go ahead, nobody's stopping you.