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Old 2003-12-10, 21:53   #1
bailrs
 

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Default 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?
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Old 2003-12-10, 21:56   #2
Wacky
 
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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.
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Old 2003-12-10, 22:00   #3
Prime Monster
 
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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
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Old 2003-12-12, 04:07   #4
wblipp
 
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Note that we usually indicate exponentiation with "^", although it also works to write [ sup ]exponent[ /sup ] so it shows asexponent.

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

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 2M40-1 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.

Last fiddled with by ewmayer on 2005-12-28 at 21:42 Reason: Edited to reflect merging of 2 similar threads
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Old 2003-12-13, 03:06   #5
cheesehead
 
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"Richard B. Woods"
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Default Re: so is it so easy?

Quote:
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:

220996011-1 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 220996011-1 is prime, the largest known Mersenne prime was 213466917-1, 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 213466917-1 and 220996011-1. 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 220996011-1 (and there's even a small chance that the next Mersenne prime to be discovered will be less than 213466917-1).

So, as well as testing numbers larger than 220996011-1, 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 220996011-1.

Does this answer your questions?
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Old 2003-12-13, 04:52   #6
calder
 

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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?
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Old 2003-12-13, 05:21   #7
wblipp
 
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Quote:
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.
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Old 2003-12-13, 05:37   #8
GP2
 
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Quote:
Originally posted by calder
why dont we just calculate this:


....20996011-1
..2
2
First of all:

1) if P is not prime, then 2P-1 can't be prime.
2) if P is prime, then 2P-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
22[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).
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Old 2003-12-13, 17:55   #9
calder
 

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o, i get it now.... :>
but how about the money? do we share if i find it out or its just mine?
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Old 2003-12-13, 18:03   #10
nfortino
 
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We share. The rules are posted at http://www.mersenne.org/prize.htm
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Old 2003-12-14, 23:26   #11
QuintLeo
 
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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....
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