New 17 million-digit prime number

Recent news announced the discovery of a new Mersenne prime. What was interest was the response I saw on some of the boards that where reporting this news, for example:

“but can someone explain how digging up mersene prime numbers helps contribute to the betterment of humanity?”

…”but is there any point to this, beyond curiosity?”

“While this is cool, how exactly does this benefit society?”

The question is, if something doesn’t have an immediate application, is it worth doing, especially if if involves tax dollars? One answer is no, federal tax dollars should only be used to fund work that has immediate benefits to society. This would mean that the bulk of basic research would stop. The private sector that includes companies and volunteer individuals would not be able to fill the gap. One possibility is to add an incentive that would allow basic discoveries to be protected by law. For example if someone discovers the relation F = ma, they should be able to collect royalties from anyone who needs to handle motion in a predicable way, that would include the military, aerospace and many many other industries. In this case the royalties could be enormous, a real incentive to make basic discoveries. Another example, someone discovers a new prime number, modern communications that requires security could pay royalties to use that number. Someone discovers the structure of DNA, that would be a real money spinner. Protection of basic research IP would however have to be at least 100 years long because many basic discoveries do not find applications for a long time. On the other hand if money where the only driver would someone put the effort in to doing expensive basic research when the payback might take 100 years or possibly not at all?

The second option is to keep things as they are. The level of investment by the federal government is tiny compared to the overall budget. The NSF which supports basic research across all non-health related disciplines spends about 6 to 7 billion per year. To put that in perspective, that is about 0.2% of the total federal budget. Of health related basic research, roughly 3 to 4 billion is spent by the NIGMS, about 0.1% of the total federal budget. Other agencies such as NASA and DOE also provide small amounts of funds for basic research. The total figure is most definitely less than 1%. For the NSF the funds amounts to about 13 cents per day per tax payer. One Starbucks tall latte at $3 a cup would pay for 23 days of NSF funding.

In contrast the cost of two recent and famous wars is roughly 1.5 trillion over ten years (http://costofwar.com/, http://economistsview.typepad.com/economistsview/iraq/). That amounts to about $2.93 per day per tax payer. Similar comparisons could be made with other budgets but at the end of the day it is a matter of priorities and where we think tax dollars should be spent.

Figures assume 140 million tax payers and total federal expenditure of about 3 trillion per year.

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