Mersenne-Number Notation?

What does M25839277 mean? I'm currently a high school student and have not had a math class that has anything like that in it. Can someone explain it (in COMMON ENGLISH) please?

[Uncwilly]

M25839277 is shorthand. It actually should be written as:

M(25839277)

That means that we are taking 25839277 and putting it through some function (mathematical process) called M. We are using M because it is a Mersenne number (named after a person with the last name of Mersenne).

The M function is:
M(25839277) = 2^25839277-1

That gives us an enormous number, because we are taking 2 and multiplying it by itself 25839277 times, then we take that number and subtract 1 from it (giving us an odd number).


Some times we get real lazy and refer to the M numbers that are prime by their place in the list of Mersenne primes (1 being smallest and getting bigger). For example M38 general is use to refer to the 38th known Mersenne prime and not M(38) (which can't be prime).



PS: If you don't understand how I or anyone explains this, tell us, we can restate it so that you can.

BTW: to get an idea how big of numbers we are talking about:
M(20,996,011) is 6,320,430 decimal digits long (meaning written out like most people write numbers)
M(24,036,583) is 7,235,733 digits long. (it would take 1290 sheets of paper to type it out with a typewriter if you filled the entire page with numbers, 85 digits across and 66 lines)

Lol, I didn't need QUITE that much of an explanation. I know quite a bit about exponents and how they work, I just didn't know what the 'M' meant, or what sort of function it was performing. Thanks though for clearing that up :). And by the way, big numbers were at one time a sort of hobby for me. I kind of had an obsession with them...numbers even bigger than 2^~24,000,000. Are there any supercomputers working for GIMPS? They would accomplish in minutes and hours what takes (most) of the rest of us weeks and months.

[cheesehead]

Originally Posted by Unregistered

Are there any supercomputers working for GIMPS?

I don't think so.

Actually, GIMPS was organized to allow personal computers to cooperatively compete with supercomputers in the search for Mersenne primes.

If you peruse a history of Mersenne prime discoveries (e.g., http://www.utm.edu/research/primes/mersenne/index.html), you'll find that the most recent discovery of a Mersenne prime by a supercomputer was in 1996, just before the first discovery of a Mersenne prime by GIMPS, and that all subsequent discoveries have been by GIMPS!

They would accomplish in minutes and hours what takes (most) of the rest of us weeks and months.

You mean, "... what takes (most) of the personal computers of the rest of us ...", I think. Personally, it would take me hundreds of thousands of years on my own ...

[M29]

Originally Posted by Uncwilly

That gives us an enormous number, because we are taking 2 and multiplying it by itself 25839277 times, then we take that number and subtract 1 from it (giving us an odd number).

Actually, since 2^2 is multiplying 2 by itself 1 time, we are taking 2 and multiplying it by itself 25839276 times (then subtracting 1 making it odd).