The main reason is that proof-of-work solutions should be hard to find and easy to verify. Mersenne primes are hard to verify. For instance, if I told you that 2^99999989 - 1 is prime, you have no way of knowing whether I'm lying or not without spending ages running the Lucas-Lehmer primality test. -- APG.
Sent: Sunday, December 23, 2018 at 10:52 PM From: "Henry Baker" <hbaker1@pipeline.com> To: math-fun@mailman.xmission.com Subject: [math-fun] New Mersenne; GIMPS Coin? Why not GIMPS for POW?
FYI --
A dozen Mersenne Primes in 15 years isn't exactly the same as a new blockchain block every 10 minutes, but at least it isn't consuming as much electricity as a third world country.
Why not use GIMPS as proof-of-work for a "coin" that is only minted ~1X per year?
We already have *sharing arrangements* to spread the wealth among all of the searchers of other blockchain coins, so this sort of arrangement should also work for GIMPS.
https://www.mersenne.org/primes/?press=M82589933
https://science.slashdot.org/story/18/12/22/2130212/51st-known-mersenne-prim...
The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^82,589,933-1, having 24,862,048 digits. A computer volunteered by Patrick Laroche from Ocala, Florida made the find on December 7, 2018.
GIMPS has been on amazing lucky streak, finding triple the expected number of new Mersenne primes -- a dozen in the last fifteen years.
Patrick Laroche is one of thousands of volunteers using GIMPS' free software to hunt for prime numbers -- and is now eligible for a $3,000 "research discovery award," the group writes at mersenne.org.
--- Perhaps it would be better for GIMPS if we *were* in Kansas anymore:
https://yro.slashdot.org/story/18/12/22/2029247/kansas-is-trying-to-unload-1...
Kansas Governor Jeff Colyer's administration is seeking a way to donate or sell at a steep discount as much as $10 million in unused computer equipment that has been stored in a state office building since 2016. The state still owes $2 million on the equipment, which it bought in 2016 as part of a failed plan to develop a centralized storage system, call Kansas GovCloud, for computer information. That idea was canceled by state IT officials who said it was too expensive. Instead, the state contracts with an outside company to store data on remote servers.
Attempts to sell the equipment failed to attract bidders, leading to discussions about finding someone to take the equipment before its value dropped to the level of scrap metal...
[I seem to recall that between manufacturing and delivery, the old DEC computers were constantly working on GIMP-style problems; with today's blockchain mining apparatus, yet-to-be-delivered & warehoused computers could be earning their keep.]
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