prime 95 notation

[spyros]

hello i am new in this forum
i get "trial factoring M58707931 to 2^69 x% complete" messages
what M58707931 to 2^69 standard notation is?
thank you

[spyros]

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

[10metreh]

Originally Posted by spyros

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

Don't you know what the % symbol means?

[spyros]

i am asking what is the meaning of "M58703971 to 2^69"?

[TimSorbet]

I'll break it down:
Trial factoring means dividing by many small numbers to see if any divide the large number. For more info about how the number is quickly divided (among other GIMPS-related mathematics) see http://v5www.mersenne.org/various/math.php
M58707931 means 2^58707931-1. For general info on Mersenne numbers see Mersenne prime
2^69 means 2 times itself 69 times.

So "trial factoring M58707931 to 2^69" means we're dividing 2^58707931-1 by every number between 2^68 and 2^69 (the numbers below 2^68 have already been checked) to see if any divide the number exactly. If any do, then we know that the number is not prime.

[Uncwilly]

Originally Posted by Mini-Geek

So "trial factoring M58707931 to 2^69" means we're dividing 2^58707931-1 by every number between 2^68 and 2^69 (the numbers below 2^68 have already been checked)

all potential factors

[Uncwilly]

Originally Posted by spyros

i am asking what is the meaning of "M58703971 to 2^69"?

Your answer has been given in the thread that you started.
http://www.mersenneforum.org/showthread.php?p=177872
go there for the answer.

[spyros]

i see.
There may be other prime numbers between merssenne primes?

[ATH]

2^58707931-1 might be prime. The first check is testing all numbers up to a certain limit to see if they are a factor of 2^58707931-1.

Then Prime95 does a longer test called P-1 to test for larger factors, and finally if we still don't know any factors, Prime95 starts the long primality test which is called Lucas-Lehmer test (LL test).

[Uncwilly]

Originally Posted by spyros

There may be other prime numbers between merssenne primes?

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

[Uncwilly]

Originally Posted by ATH

2^58707931-1 might be prime. The first check is testing all numbers up to a certain limit to see if they are a factor of 2^58707931-1.

Again all potential factors of the given prime ar checked (up to the size mentioned). If you see the math section referenced above, you will see that any pontential factor is a function of the exponent (58707931 in your case), this makes it easier to check for factors.