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 2009-08-20, 23:40 #1 heich1   Aug 2009 1910 Posts How Many Mersenne Numbers Left Exponent<10000000 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?
2009-08-21, 01:09   #2
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

17E816 Posts

Quote:
 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.

2009-08-21, 02:16   #3

"Richard B. Woods"
Aug 2002
Wisconsin USA

170148 Posts

Quote:
 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).

"... 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.

2009-08-21, 02:19   #4

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 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?

2009-08-21, 02:26   #5
retina
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"The unspeakable one"
Jun 2006
My evil lair

23·32·5·17 Posts

Quote:
 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.

2009-08-21, 04:57   #6
Kevin

Aug 2002
Ann Arbor, MI

433 Posts

Quote:
 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.

2009-08-21, 21:17   #7

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 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.

Quote:
 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.

Last fiddled with by cheesehead on 2009-08-21 at 21:32

 2009-08-21, 21:45 #8 heich1   Aug 2009 19 Posts How Many Mersenne Numbers Left Exponent<10000000 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?
2009-08-21, 21:57   #9
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17×251 Posts

Quote:
 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?
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.

Last fiddled with by Mini-Geek on 2009-08-21 at 22:07

 2009-08-22, 09:44 #10 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2×29×101 Posts http://www.mersenneforum.org/showthread.php?t=11292 might interest you.

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