
New prime record: 51st Mersenne prime - chmaynard
https://www.johndcook.com/blog/2018/12/22/51st-mersenne-prime/
======
ChrisSD
Previous discussion:
[https://news.ycombinator.com/item?id=18736880](https://news.ycombinator.com/item?id=18736880)

------
speps
Given that the finder of a new prime gets a $3000 award, can someone do the
math and see if running Prime95 is actually better than playing the lottery?

~~~
schoen
I think there's a simple calculation to estimate that the expected financial
value of running Prime95 (just for this particular prize) is negative.

Suppose GIMPS as a whole discovers one new Mersenne prime per year and pays
its discoverer $3000. According to
[https://www.electricchoice.com/electricity-prices-by-
state/](https://www.electricchoice.com/electricity-prices-by-state/), the
average U.S. residental customer pays 13.11 cents per kilowatt-hour for
electricity.

Suppose that you wanted to run a desktop computer with Prime95, hypothetically
consuming 80 watts (which is probably low).

    
    
      You have: 13.11 cent/kWh
      You want: dollar/(80 watt*year)
      	* 91.935844
    

So it's going to cost about $91 to run that computer for a year, which means
that your net earnings are negative in expectation if your computational
contribution to GIMPS from that machine is less than than 3000/91 or about
1/33 of the network's total computational power.

There are lots of ways to make this estimate better, for example by finding
the actual fraction of computational capacity that an individual machine
contributes, or the actual power consumption of that machine, or the actual
cost of electricity for that machine's owner, or a better estimate than "one
per year" of the GIMPS discovery rate (for example, their current press
release says that recently they've found about three times as many primes as
they expected).

~~~
mhh__
So you're saying I need to use someone else's computer?

~~~
schoen
This is a real phenomenon that people used to get in trouble for back before
the days of cryptocurrency mining.

For the EFF cooperative computing awards, we have a provision about this:

> EFF reserves the right to require a more detailed disclosure. For example,
> EFF may require evidence that the hardware was used legally, with the
> owner's permission and support.

[https://www.eff.org/awards/coop/rules](https://www.eff.org/awards/coop/rules)

A particularly notable case where someone was accused of unauthorized computer
use for running a distributed computing client back in 2001:

[https://www.extremetech.com/extreme/49898-georgia-cracks-
dow...](https://www.extremetech.com/extreme/49898-georgia-cracks-down-on-
distributed-computing)

------
torbjorn
Mersenne primes can be written as: 2^(some prime) - 1. Is there a name for the
primes that can be written as: 2^(some prime) + 1?

~~~
zamadatix
Interestingly there are only 6 known primes of the form 2^n+1. Other than "2"
these are all Fermat primes of the form 2^(2^n)+1 and so there is only a
single known case n is prime - the case of n=2.

[https://oeis.org/A092506](https://oeis.org/A092506)
[https://oeis.org/A019434](https://oeis.org/A019434)

------
raister
That's odd.

~~~
wlll
Oh my.

