No need to be hopeless about winning one of these! The "easiest" ones to target, I think for the general HN crowd, will be the EFF Cooperative Computing Awards, i.e. finding primes with 100 million and a billion digits. Looking at the winning claim from 2009 (https://www.eff.org/awards/coop/primeclaim-43112609), which was a Mersenne prime with 12M+ digits, I see that it was discovered using an "Dell Optiplex 745 computer with an Intel Core 2 Duo E6600 CPU running at 2.4 GHz" running for about 33 days. Netting the 100M prime should be doable using, e.g. a couple hundred EC2 instances for a couple of weeks.
With current EC2 prices (http://aws.amazon.com/ec2/pricing/) , for $100k one can run a c4.8xlarge instance (36 cores) for 2244 days, so for a comparable time for the 2009 award, you can run (2244/33)x36=2448 cores rather than two. Assuming that's adequate to discover the 100M digit prime, that's a net profit of $50k!
Since no body has done this there must be some significant flaws in the naive analysis above. What are they? What is a rough estimate of how fast the computational load would go up from 10M to 100M to 1B digit prime search?
I think you misread how the previous prime was found:
"4D. The Lucas-Lehmer test began on Sun Jul 20 12:33:46 2008 PDT and concluded on Sat Aug 23 00:29:27 2008 PDT. That's a total of 33 1/2 days. The Dell Optiplex was the only computer used to initially prove this candidate prime. However, the computer was part of GIMPS' "PrimeNet" network of roughly 75,000 computers testing other Mersenne number candidates."
It didnt take one computer 33 days, it took 75,000 computers searching simultaneously to find a prime.
edit: The next largest prime, at 17 million digits, took a further 5 years of searching on a network that has over 100 TFLOP/s of compute power [1].
The choice of a Dell Optiplex business desktop PC for a month-long calculation in 2008 is interesting for historical reasons.
A decade before that, Sun workstations that cost $30k each were used for long-running engineering tests like chip verification, while an Optiplex is less than 10% of that.
Well, in 1998, I was running a dual-processor Dell Optiplex at 400MHz for month-long simulations; it cost $5000 at the time. but yeah, most people around me were buying $25k SGIs that had about half the oomph of my machine. I think that was the year it became clear Intel was going to get enough floating point and cache to be competitive with the RISC UNIX systems.
At the bottom there is a list of "solved problems". I was surprised to read,
Brexit Prize
by Institute of Economic Affairs
2013 - 2014
€100,000
Find the best plan for a UK exit from the European Union.
I was surprised, because my own personal opinion is that that's a pretty stupid idea (UK exit from the EU). Since I'm a super, super open-minded guy I decided to embetter my worldview and read the paper, since, you know, if it's in company like the "longitudinal prize" then hell, maybe 1) I'm wrong and 2) I'll learn something.
Folks, this is 15,000 words. That means he got paid $6 per word to write that. I personally skimmed the PDF, didn't find anything that caught my eye or even a point, based on the the abstract or the section titles and the whole framing, and wasn't left with the impression that the author even believed it. Perhaps his 15,000 word PDF won simply because nobody else bothered to put a plan together, not because there's anything great or wortwhile about such a plan.
So forget "lander on mars". Win a prize that consists of a meaty term paper on some stupid proposition. A+ as a term paper, though.
I was surprised with that entry too, however not because of the specifics (UK exit from EU, which I happen to agree with), but rather that it is the only prize with some sort of political outcome. All of the other prizes have some basis in math, science and technology with well defined criteria for winning. A political outcome is almost by definition subjective.
The competition wasn't really about whether the UK should go or not, which is the main political part. Rather, the starting point is that a referendum has decided "go", and the competition was to find the best way of extricating the UK from existing institutions/agreements, what should replace them, and how.
However, the remit is very unclear on the criteria used to judge entries.
With current EC2 prices (http://aws.amazon.com/ec2/pricing/) , for $100k one can run a c4.8xlarge instance (36 cores) for 2244 days, so for a comparable time for the 2009 award, you can run (2244/33)x36=2448 cores rather than two. Assuming that's adequate to discover the 100M digit prime, that's a net profit of $50k!
Since no body has done this there must be some significant flaws in the naive analysis above. What are they? What is a rough estimate of how fast the computational load would go up from 10M to 100M to 1B digit prime search?