Prime numbers are tricky things. They are one of the most fundamental parts of our numerical systems, but they're difficult to predict.

You would kind of expect that something so elementary should be easily predictable, or follow a pattern. But while we've found some similarities (like the mersenne primes) there's still a kind of nagging feeling that there should be a more basic way to enumerate prime numbers than guess and check.

We've learned some simple things about them, such as the existence of Mersenne primes, or ideas on the probability of any given number being prime being inversely proportional to its logarithm.

But I think the biggest thing is that it's a puzzle. But a puzzle that bothers us because it seems like it should be easy to solve, but it's not.

Finding larger prime numbers tells us more about them. It lets us see other parts of patterns. Patterns that might lead to some insight on how to predict if a number is a prime, or how to factor large numbers. This might have an impact on cryptography for instance.

But finding this number doesn't solve a problem, it adds to a body of knowledge. It fills in a bit of the puzzle. In the end the hope is that we learn something about the puzzle, or at the least, learn why we can never learn something about the puzzle.

I am curious too. I wonder if this has anything to do with the public key encryption relying on prime numbers.

EFF has a bounty for large prime numbers: https://www.eff.org/awards/coop

"The EFF awards are about cooperation," said John Gilmore, EFF co-founder and project leader for the awards. "Prime numbers are important in mathematics and encryption, but the real message is that many other problems can be solved by similar methods."

Finding these prime numbers will be no simple task, given today's computational power. It has taken mathematicians years to uncover and confirm new largest known primes. However, the computer industry produces millions of new computers each year, which sit idle much of the time, running screen savers or waiting for the user to do something. EFF is encouraging people to pool their computing power over the Internet, to work together to share this massive resource. In the process, EFF hopes to inspire experts to apply collaborative computing to large problems, and thereby foster new technologies and opportunities for everyone.

> However, the computer industry produces millions of new computers each year, which sit idle much of the time, running screen savers or waiting for the user to do something.

Considering how much more electricity a running computer uses versus an idle one and how much faster consumer CPUs degrade under load this definitely seems like a huge waste of resources for something that has little, if any, utility.

I used to run prime95 on all of my machines, back when power management (especially on desktops) was virtually nonexistent. Obviously, with the power management features we have now, an idle CPU (especially outside of a hosting environment) is not considered wasteful.

This sort of thing is comparable to sending humans to the Moon. In and of itself, there's not much of a point to it; but the technology you develop to get there has a tendency to become useful in other, perhaps more useful, areas.

In the case of the Mersenne prime hunt, you need the fastest integer multiplication algorithms (and concrete implementations) you can. Fast integer multiplication is a big part of several useful number-theoretic algorithms. An interesting (to me) application is, for example, to check whether a number is only divisible by small primes. This is an integral part of the most efficient integer factorization algorithms known, and one way to do it is with a product tree followed by a remainder tree [1]. This would be unacceptably slow without quasilinear-time multiplication algorithms.

[1] https://cr.yp.to/lineartime/multapps-20080515.pdf

I like this Moon analogy you've made. I'm sure it's a broad stroke but still serves as a simple and effective answer to the question. Thanks.

One of the key features of pure mathematics is that we come up with results just to have sitting around, on the off chance they ever become useful. And often they do, much later on. It’s a gift to the future.

In 1940, Hardy used the theory of numbers as an example of a profoundly and permanently useless discipline in A Mathematicians Apology[1]. The fact that number theory is the basis for modern cryptography gives the lie to this sentiment.

The fact is that we don't know whether the search for Mersenne primes, or any other mathematical endeavour, will reveal anything useful, but given the depth of interconnection between different branches of mathematics and the usefulness of some of those branches, it doesn't seem plausible that we won't find useful things.

Although Hardy turned out to be wrong about number theory and its applications, his arguments for the intrinsic value of the study of mathematics in the absence of any real utility stand as well.

And of course, as another commenter has pointed out, making computers do things like this is a great way to develop phenomenally fast and useful algorithms.

Finally, the project found a bug in Intel CPUs[2], which is kind of neat...

[1] https://www.math.ualberta.ca/mss/misc/A%20Mathematician's%20... [2] http://www.extremetech.com/computing/220953-skylake-bug-caus...

I assume it's somewhat academic in nature, but I could speculate it may have some cryptography applications where Prime's are used heavily.

It's similar to Barry Bonds hitting the most home runs. It serves the world nothing but lots of exercise for Barry, but it's an achievement that everyone can feel proud about. In addition, the GIMPS project has contributed to an efficient FFT and to distributed computing research.

It's purely academic.