How Many Mersenne Numbers Left Exponent<10000000

[heich1]

I would be interested to find out how many Mersenne Numbers are left that have an exponent less than 10,000,000. I know that today, August 20th, 2009 it is between 352 and 770 fot the initial check, i.e. the numbers unchecked for M(32582657) and M(37156667). Also, how do you find this number?

[retina]

Originally Posted by heich1

I would be interested to find out how many Mersenne Numbers are left that have an exponent less than 10,000,000.

Are left for what? I assume you are asking about how many left for testing to find a prime? All exponents less than 10M have been fully checked and double checked. There are none left to test unless you want to test something for another purpose other than finding a new prime.

[cheesehead]

Originally Posted by heich1

I would be interested to find out how many Mersenne Numbers are left that have an exponent less than 10,000,000. I know that today, August 20th, 2009 it is between 352 and 770 fot the initial check, i.e. the numbers unchecked for M(32582657) and M(37156667). Also, how do you find this number?

First of all, I need to clarify your question.

I'm guessing that when you write:

"... how many Mersenne Numbers are left ..."

you mean"

"... how many Mersenne numbers are left to be tested ..."

Also, I think you may be confusing two different things:

a) the exponent of a Mersenne prime (or any Mersenne number), and

b) the number of digits in a particular Mersenne prime (or any Mersenne number).

Your posting leads me to guess that when you wrote:

"... how many Mersenne Numbers are left [to be tested] that have an exponent less than 10,000,000."

you meant:

"... how many Mersenne Numbers are left [to be tested] that have fewer than 10,000,000 digits in their decimal form".

So what you're asking for is:

"Where can I find out how many of the Mersenne Numbers that have fewer than 10,000,000 digits in their decimal form are not yet tested? (Both first-test and DC)

Assuming I'm right, what you need first to answer that is the exponent of the first Mersenne number that has 10,000,000 decimal digits or more. It's 33219278. (That's 9,999,999 divided by the base-10 logarithm of 2, then rounded up to the next integer.) You want the number of Mersenne numbers with exponents less than 33219278 that have not yet been tested, if I'm right.

You've seen that the GIMPS milestone page at http://mersenne.org/report_milestones/ doesn't keep track of that. I don't know of any other web page that's keeping track of that, either.

Someone can go in, get a report of all the exponents not yet first-time-tested or yet DCed, and count how many of those exponents are below 33219278.

I'm going to leave it at that for now. If I can do the count, I'll post later.

If someone else knows where the counts of untested exponents below 33219278 can be found, please step in here.

[cheesehead]

Originally Posted by retina

All exponents less than 10M have been fully checked and double checked.

The question to have asked when interpreting the OP was:

Why does the OP mention M(32582657) and M(37156667), and what is their relationship to 10,000,000?

[retina]

Originally Posted by cheesehead

The question to have asked when interpreting the OP was:

Why does the OP mention M(32582657) and M(37156667), and what is their relationship to 10,000,000?

Yes you are right. I thought it was an independent question. I didn't read it thoroughly enough.

[Kevin]

Originally Posted by cheesehead

The question to have asked when interpreting the OP was:

Why does the OP mention M(32582657) and M(37156667), and what is their relationship to 10,000,000?

If you only know about the Milestones page, and not the Primenet summary page, checking how many exponents are left untested below 32582657 and 37156667 give a lower and upper bound (respectively) on how many are left untested with less than 10 million digits.

[cheesehead]

Originally Posted by Kevin

checking how many exponents are left untested below 32582657 and 37156667 give a lower and upper bound (respectively) on how many are left untested with less than 10 million digits.

... and that shows that the OP really meant to ask about numbers with fewer than 10,000,000 digits, not "exponent less than 10,000,000" as mistakenly written.

If you only know about the Milestones page, and not the Primenet summary page,

How does the PrimeNet summary page help? It shows ranges of one million of exponent value. One could interpolate to get an estimate for the number below 33219278, but not an exact count, and even the estimate would require some assumption about the distribution in the 33000000-34000000 range.

Do you mean some other PrimeNet page than http://mersenne.org/primenet/ or am I missing something?

- - -

One solution would be to add countdowns for exponents delimiting 10,000,000-digit (and 100,000,000-digit) numbers to the milestone list.

[heich1]

Sorry I meant how many Mersenne Numbers are left to be tested as prime by GIMPS that have an exponent less than 100,000,000? Also how do you find this number?

[Mini-Geek]

Originally Posted by heich1

Sorry I meant how many Mersenne Numbers are left to be tested as prime by GIMPS that have an exponent less than 100,000,000? Also how do you find this number?

See this page: http://mersenne.org/primenet/
You should be able to figure it out quite easily. Here's a hint: Look at the Status Unproven section up through 100,000,000.

[henryzz]

http://www.mersenneforum.org/showthread.php?t=11292 might interest you.