Is 2^{mersenne prime}-1 prime?

why the new prime number as an exponent for 2 ^X - 1 does not work as the largest number?

As I understand the exponent must be prime which this new number is, so why does it not work?

[Wacky]

That the exponent is prime is a necessary, but not sufficient condition.

2^(M40) -1 may be prime. But it is too large for us to test.

[Prime Monster]

Not all prime numbers will generate Mersenne primes. The range we are working on now is somewhere between 20 and 22 million ( 33 million + for the oines that are goiing for the big price). 77 million is about the top end of the range we can work on with todays client.

All these numbers have 8 digits in the exponent. The newly found prime has 6,320,430 digits, and a potential Mersenne generated from that would be unbelievably huge.

PM

[wblipp]

Note that we usually indicate exponentiation with "^", although it also works to write [ sup ]exponent[ /sup ] so it shows as^exponent.

Then the questions are "why not just calculate 2^M40-1?" and "Are we calculating 2^M40-1?"

The core issues are that a prime exponent is necessary to get a prime but not sufficient - that is, not all prime exponents generate prime numbers, so we must test each one, and 2^M40-1 is much too big to be tested by any known methods even using all the computing power in existence. So no, we are not testing that. We are mostly testing prime exponents a little bit larger than the exponent that lead to the recent prime. Some people are double-checking smaller exponents because about 2% of tests have errors. A few people are checking prime exponents for numbers that have over 10 million digits.

[cheesehead]

Originally posted by calder
why dont we just get a computer that calculats


(the largest now)
2 -1?
i know its gota take some time but it will be much faster if some one get a super computer and do it.......
so every time we can get much better other than 1 by 1.....

We're not completely sure what you mean, but I'll take another stab at it and maybe this is your answer:

2^20996011-1 is the largest known Mersenne prime now. (We're pretty sure there are other Mersenne primes that we don't yet know.) Before we proved that 2^20996011-1 is prime, the largest known Mersenne prime was 2^13466917-1, and before that one was found to be prime, a still smaller number was the largest known Mersenne prime.

But not all Mersenne primes have been discovered in numerical order. At least once in the past, someone found a Mersenne prime that was smaller than the largest known Mersenne prime as of that date ... because the discoverer of the then-largest one had skipped testing some smaller candidates.

GIMPS has not yet finished testing all the possible Mersenne primes between 2^13466917-1 and 2^20996011-1. Because GIMPS participants use a wide variety of computers, some much faster than others, and for other reasons, the tests are not necessarily completed in numerical order. It is possible that the next Mersenne prime to be discovered will be smaller than 2^20996011-1 (and there's even a small chance that the next Mersenne prime to be discovered will be less than 2^13466917-1).

So, as well as testing numbers larger than 2^20996011-1, we have to finish testing (or even re-test, if there is an error in a test) many of the smaller numbers before we can conclude that the next Mersenne prime is larger than 2^20996011-1.

Does this answer your questions?

what i mean is that : ( i dont now how u did the power on this thing)


why dont we just calculate this:


....20996011-1
..2
2

we know its a prime for sure, because 2p-1 is a prime......
so why dont we just use the largest we know now as a power of 2 then -1... and just calculate that?

[wblipp]

Originally posted by calder
we know its a prime for sure, because 2p-1 is a prime......

We don't know it's a prime. GIMPS has spent two years checking prime exponents to find another Mersenne Number that is prime - most prime exponents do not result in prime Mersenne Numbers.

[GP2]

Originally posted by calder
why dont we just calculate this:


....20996011-1
..2
2

First of all:

1) if P is not prime, then 2^P-1 can't be prime.
2) if P is prime, then 2^P-1 might be prime, but not necessarily (in fact, the odds are very low).

Second of all:

It's hopeless to even think about doing a Lucas-Lehmer test on such an enormous number. There isn't enough time between now and the end of the universe, and not enough atoms in the universe to build a computer that could do it.

Even
2^2[sup]61-1[/sup]-1
is far too big (see http://www.ltkz.demon.co.uk/ar2/mm61.htm).


PS,
To do exponents, just use [ sup ] and [ /sup ] (except without the blanks next to the brackets).

o, i get it now.... :>
but how about the money? do we share if i find it out or its just mine?

[nfortino]

We share. The rules are posted at http://www.mersenne.org/prize.htm

[QuintLeo]

If GIMPS was ranked as a supercomputer on the "Top 500 supercomputers" list, IIRC we'd be somewhere in the top 10 or 15 *already*.

To be fair, if all of the other large projects like SETI and Distributed.Net got ranked on that list, we'd drop a few places - I suspect SETI and D.Net EACH harness more overall CPU power than the Earth Simulator (the highest-power supercomputer on that list)....

So just adding one "supercomputer" wouldn't make things a lot faster - in effect, we're *ALREADY* a supercomputer, of a widely-distributed nature....