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Old 2007-11-04, 18:38   #1
rong123
 
Nov 2007

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Question Question about Mersenne Numbers

Hi all,

I am kinda new to Prime95 and all but am very interested in the hunt for new prime numbers and I have a question. I am wondering firstly, is there a simple program that can generate a Mersenne number for the bit depth specified? I mean of course a Mersenne number at its lowest to that depth like: If I say for instance want a MErsenne number that is 1 billion digits like 2^1000000000-1 or whatever.. I want the lowest number to the 1 billionth exponent that is Mersenne, then the next highest number that is Mersenne above the lowest, etc, etc. OR say for instance I put in like 1 million exponent it would spit out the lowest Mersenne number that is closest to 1,000,000th exponent, then upwards from there in chronological order. I have looked all over the web and can not find a list of Mersenne numbers (not talking about the ones proven to be prime already) just a list of all mersenne numbers, or a program that can generate mersenne numbers woudl be great! Sorry I am not a mathmetician or anything, i'm a complete newb, so my explanation may not be the greatest hehe....Any help would be greatly appreciated....I am kinda interested in starting factoring for the billionth mersenne prime search and I would like to know the lowest, next lowest, etc then decide which I may wanna start factoring as a start on my own little project..

Also would it be like this when doing Mersenne trial factoring... I find the billionth number for instance, then take that number say its n then do a Factor=n^1, then n^2, ....n^72 in that order??...I see on the billion project where they start at like n^74 then have worked down to like n^71 or so.. wouldnt it be more logical to start at n^1 then work up to n^74, n^75, etc? when factoring?...Maybe I'm all wrong in my thinkiology here but just figuring all this stuff out..

THX~!

Ron G
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Old 2007-11-04, 22:59   #2
jasong
 
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First, welcome to the Forum. I'm going to try to answer your questions before someone only skims your post and decides to flame you.
Quote:
Originally Posted by rong123 View Post
I am kinda new to Prime95 and all but am very interested in the hunt for new prime numbers and I have a question. I am wondering firstly, is there a simple program that can generate a Mersenne number for the bit depth specified?
[quote]I'm sure there are people here who can help you with that. If you just want to get in the general area of a digit level, than <digit level>/log(2) would work. For instance to find the first 1,000,000-digit Mersenne, 1,000,000/log(2) is about 3321929, or thereabouts.
Quote:
I am kinda interested in starting factoring for the billionth mersenne prime search and I would like to know the lowest, next lowest, etc then decide which I may wanna start factoring as a start on my own little project..
Judging from the stuff you wrote before this, I believe you've misspoke. The billionth Mersenne NUMBER would be a bit easier than the billionth Mersenne prime. It would simply be a matter of identifying the billionth prime(regular prime) and plugging that as n into 2^n-1.

Quote:
Also would it be like this when doing Mersenne trial factoring... I find the billionth number for instance, then take that number say its n then do a Factor=n^1, then n^2, ....n^72 in that order??...I see on the billion project where they start at like n^74 then have worked down to like n^71 or so.. wouldnt it be more logical to start at n^1 then work up to n^74, n^75, etc? when factoring?...Maybe I'm all wrong in my thinkiology here but just figuring all this stuff out..
Not totally sure what you're referring to, but that's okay.

Since Mersenne numbers are of a special form, we can make assumptions about their factors. Unfortunately, I'm not totally certain what that form is, so I'll let someone else tackle that. I will say that a TON of numbers are disqualified through number theory, making it literally millions of times faster to find a factor for a Mersenne number than if we simply tried all the primes in a given range.

Last fiddled with by jasong on 2007-11-04 at 23:00
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Old 2007-11-04, 23:17   #3
paulunderwood
 
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Quote:
1,000,000/log(2) is about 3321929, or thereabouts.


Code:
? log(10)/log(2)*10^6
3321928.0948873623478703194294893901759
naturally

Last fiddled with by paulunderwood on 2007-11-04 at 23:29
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Old 2007-11-05, 05:38   #4
rong123
 
Nov 2007

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Doh sorry, I was actually meaning to ask what would be the first billionth Mersenne number? so would it be like this ? 1,000,000,000/log(2)= 3321928094.89. I am assuming I would not need to .89 at the end? So could I say this as an exponent like this 2^3321928094-1 ? or would i need to use the decimal number also ?

quote:
Judging from the stuff you wrote before this, I believe you've misspoke. The billionth Mersenne NUMBER would be a bit easier than the billionth Mersenne prime. It would simply be a matter of identifying the billionth prime(regular prime) and plugging that as n into 2^n-1.

No I was referring to the billionth exponent Mersenne Number ( a Mersenne number with and exponent in the billions that has not been proven yet) ..if I wanted to see if this Mersenne number was a Mersenne Prime?

So if the number above was indeed the lowest 2^n-1, n=M3321928094, Would I be able to start factoring this Mersenne number using trial factoring? Like I was saying in my original post Factoring all the way up to something like n^74 starting in the chronology like i was saying n^1, n^2...etc? Like when Prime95 grabs an assignment for trial factoring and puts it on your worktodo.ini example: Factor=3321928094,1 then Factor=3321928094,2 etc.. Factor=3321928094,74 OR do I have this all wrong? I am using the Factor=n thinking it is the same as what I was saying above being n^1, n^2, etc..n^74

Sorry if I am asking lame questions but as I said before I am trying to learn=) Thank you for taking the time to answer my questions

RonG
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Old 2007-11-05, 06:04   #5
jasong
 
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You're in the wrong forum.

Go to the top of the page, click on 'Factoring projects' then click on the Forum 'Lone Mersenne Hunters.'

At that point, it's simply a matter of reading the Stickies and following the instructions.

VERY IMPORTANT THING TO NOTE: Every time the bit depth increases by 1, that bit depth takes twice as the previous bit depth. Although the size of the Mersenne number exponent matters as well. If you're sieving at, say, 55 bits on a Mersenne number with an exponent around 30-million, it's going to take half as long as sieving an exponent around 15-million for that same bit depth.

Also, you might need special software for the really high sieving.
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Old 2007-11-05, 12:14   #6
Mini-Geek
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Quote:
Originally Posted by rong123 View Post
So if the number above was indeed the lowest 2^n-1, n=M3321928094, Would I be able to start factoring this Mersenne number using trial factoring? Like I was saying in my original post Factoring all the way up to something like n^74 starting in the chronology like i was saying n^1, n^2...etc? Like when Prime95 grabs an assignment for trial factoring and puts it on your worktodo.ini example: Factor=3321928094,1 then Factor=3321928094,2 etc.. Factor=3321928094,74 OR do I have this all wrong? I am using the Factor=n thinking it is the same as what I was saying above being n^1, n^2, etc..n^74
In Prime95 v24 (which is the current stable version), Factor=3321928094,2 tells Prime95 that it has been factored to 2 bits, not that you should factor it to 2 bits. What it is factored to is determined automatically, or by setting a line in the prime.ini file forcing it to factor all numbers to that bit.
In Prime95 v25 (which is an alpha preview version), you use Factor=3321928094,2,70 to say that it has been factored to 2 bits and that you want to factor it to 70 bits.

Also, for a Mersenne number to possibly be prime, the exponent must be prime. (http://en.wikipedia.org/wiki/Mersenn...ersenne_primes for a description of why) That is, in 2^n-1, n must be prime. 3321928094 isn't prime. The next prime from that is 3321928097.
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Old 2007-11-05, 17:01   #7
Jens K Andersen
 
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Quote:
Originally Posted by rong123 View Post
I was actually meaning to ask what would be the first billionth Mersenne number?
You have apparently misunderstood several things and write contradictory things so it's hard to guess what you actually want to know.

There are two different definitions of a Mersenne number:
1) A number of form 2^n-1 where n is a positive integer.
2) A number of form 2^n-1 where n is a prime number.

Please clarify which of the two you want. It has been proven that 2^n-1 cannot be prime if n is composite.

With definition 1), the billionth Mersenne number is 2^1,000,000,000-1
With definition 2), the billionth Mersenne number is 2^22,801,763,489-1 where 22,801,763,489 is the billionth prime.

Maybe you are actually looking for the smallest Mersenne numbers with at least 1,000,000,000 decimal digits? This has nothing to do with the billionth Mersenne number, no matter which definition is used.
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Old 2007-11-09, 00:34   #8
jasong
 
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Quote:
Originally Posted by Jens K Andersen View Post
Maybe you are actually looking for the smallest Mersenne numbers with at least 1,000,000,000 decimal digits? This has nothing to do with the billionth Mersenne number, no matter which definition is used.
If that's what he wants, he needs to go to the Forum 'Operation Billion Digits.'

They're factoring the lowest n-values that could possibly yield a prime that's at least a billion digits.
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