prime 95 notation

[10metreh]

Originally Posted by Mini-Geek

2^69 means 2 times itself 69 times.

It's actually 68 times. Think about it.

[joblack]

Originally Posted by Uncwilly

There are other primes between merseenes. It is just that checking mersennes is so very much easier than checking other numbers that size.

Of course - you hit these special primes only 'by accident'.

[Batalov]

Originally Posted by spyros

trial factoring is giving me messages like M58703971 to 2^69 is x%complete. what is the meaning of this?

Let's not be facetiuos.

Short answer: this is how much work was so far done on this particular bitlevel. (in your case checking all qualified k, so that 2kp+1 is in range 2^68 to 2^69). Note that every next bitlevel is roughly 2 times more work that the previous one.

Longer answer: there's a caveat in this process. Because of how the code could be best optimized, there are 16 passes, from 2^68 to 2^69 upward using different 'classes' of primes (based on residue mod 120); as you know, the possible factors must be 1 or 7 (mod 8), they can also be 1 or 2 (mod 3) and 1, 2, 3, or 4 (mod 5). So if a mersenne composite has two factors in range from 2^68 to 2^69, there's an equal chance that a larger factor will be reported first or second!

____

Ah, while I was typing... now I've looked at that other thread and realized that my typing was only an excercise for my arthritic fingers. So, yes! Let's be facetiuos.

[Batalov]

Originally Posted by spyros

trial factoring is giving me messages like M58703971 to 2^69 is x%complete. what is the meaning of this?

In simple English:
1. you signed up your computer for a job
2. you don't have to know what this job is
3. your computer received a work unit - "paint this part of the wall which is called M58703971 to 2^69, whatever that means".
4. when you look at the screen, this job is x% complete
5. when x% will reach 100%, you've done well, and your computer will receive more work
6. if you shut down your computer (or kill the program or run out of batteries, etc) before x% reaches 100% - then you will have thrown your work away. Someone else will later paint this part of the wall. Or it could be you, if/when you restart the program later.*

(ok, end of coffee break)

[Mini-Geek]

Originally Posted by Batalov

6. if you shut down your computer (or kill the program or run out of batteries, etc) before x% reaches 100% - then you will have thrown your work away. Someone else will later paint this part of the wall.

Well, this isn't entirely true. You can shut down your computer or close Prime95 and it will save its progress and continue when you let it. What you said after that part is true if you abandon the test completely before x reaches 100 and communicates with the PrimeNet server.

[spyros]

So is there a practical use for these prime numbers?

[Mini-Geek]

Short answer: no, not really
Just like there's no practical use for a million dollar diamond. Or for scaling Mt. Everest. Here's a very good list of reasons why we search for these primes:
http://primes.utm.edu/notes/faq/why.html

[Uncwilly]

Originally Posted by spyros

So is there a practical use for these prime numbers?

They can be used for encryption purposes. But it helps if you know that they are prime and any evil, middle parties don't.

[joblack]

Originally Posted by spyros

So is there a practical use for these prime numbers?

At the moment no, but as you can see very often in science: you accumulate knowledge and after some timethe pieces click together and you have new (practical) knowledge and application.