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Old 2008-09-13, 15:00   #1
retina
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Default Predict discovery date of the 1st 100M digit prime

Since we now have a 10M digit prime it is time to predict the discovery date of the first 100M digit prime.

Wild guesses are okay but it would be preferable if your guess is based upon some analysis of the various factors involved, including, but not limited to,
  • Computer speed advances
  • Computer architecture changes
  • Software improvements
  • Number of users/computers/cores searching
  • Test procedure/assignment changes
  • Other projects finding one first
  • Even future mathematical discoveries (if you feel brave to predict)
  • Any other relevant factors
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Old 2008-09-13, 16:32   #2
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initial prediction

I have some work to do to get a more accurate time but it could be sooner than we think. What I need to know most is how many Candidates their are between 1million (?????) 10million(??????) and 100million(???????) There must be a database somewhere which I will be looking for.

Based on the time required from 1million to 10million about 10 years or 2018.

nelson

Last fiddled with by Nelson on 2008-09-13 at 16:42 Reason: adjust link
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Old 2008-09-13, 16:40   #3
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There are 1,805,932 primes between 3,321,929 (the smallest exponent larger than 1 million digits) and 33,219,281 (the smallest exponent larger than 10 million digits). There are 15,852,693 primes between 332,192,810 (the smallest exponent larger than 100 million digits) and 33,219,281.

Of course, not all of these exponents are LL tested; many are eliminated through trial factoring.

Last fiddled with by jinydu on 2008-09-13 at 16:41
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Old 2008-09-13, 17:59   #4
Nelson
 
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Quote:
Originally Posted by jinydu View Post
There are 1,805,932 primes between 3,321,929 (the smallest exponent larger than 1 million digits) and 33,219,281 (the smallest exponent larger than 10 million digits). There are 15,852,693 primes between 332,192,810 (the smallest exponent larger than 100 million digits) and 33,219,281.

Of course, not all of these exponents are LL tested; many are eliminated through trial factoring.
:big grin:Now you went and spoiled all the fun. So there are only about 8-9 times as many primes to test over a range 10 times as large. I would have expected less. Well, it will be a long grind but The next Mersenne prime will help keep the irons hot and maybe we should try to predict that first. With the increase of PC power that should average out to about a year. So within the next two years we should see another one.

nelson

Last fiddled with by Nelson on 2008-09-13 at 18:04 Reason: correcting Arithmetic
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Old 2008-09-13, 19:00   #5
T.Rex
 
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Default 2023

My guess is: 2023.
Tony
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Old 2008-09-13, 21:56   #6
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Quote:
Originally Posted by retina View Post
  • Computer speed advances
  • Computer architecture changes
A significant impact on computer architecture would be if proximity communication becomes a practical option for the PC.

This would allow for fast large near die L3 caches. If it worked well today you could throw in a 256MB L3 cache for next to nothing allowing for the whole of Prime95 plus data to reside in L3 avoiding the need to go off to the high latency main memory banks.
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Old 2008-09-14, 02:00   #7
ATH
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http://v5www.mersenne.org/

If you add the columns LL-D + LL from 3,000,000 up to and including 32,000,000 you get approximately the number of LLs that has been done in the 1M-10M digit range. I get around 670.000.

Then add up the LL-ERR + NO-LL columns from 33,000,000 up to and including 331,000,000 you get approximately the number of LL-test to be done in the 10M-100M digit range. I get around 7,451,000. But we can probably subtract 15% at least because most of that range has not been factored very much. If we look at the factored (F) column divided by "Range Count" column, at 40M around 62% of the primes has factors but higher up at 100M+ the ratio is only 50% because they are only factored to 58-60bits.

So we end at around 6,333,000 LL test plus some factoring work up to 100M digit, compared to 670,000 LL test + factorting work done in 1M-10M range.
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Old 2008-09-14, 09:02   #8
Flatlander
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My guess is the 2nd half of 2015.
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Old 2008-09-14, 10:24   #9
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Quote:
Originally Posted by Flatlander View Post
My guess is the 2nd half of 2015.
You've been reading
http://primes.utm.edu/notes/by_year.html#3
haven't you?
I'm inclined to suggest that during the nine years since
the first 1M digit prime was discovered, GIMPS enjoyed a one-off
escalation in participation.
BTW in another list, Chris Caldwell opined that these latest two primes
were overdue. I had to disagree with him.

David
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Old 2008-09-14, 11:47   #10
jinydu
 
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Caldwell has been posting somewhere?

Speaking of Caldwell, his section on the size of M45 doesn't look right. He types "So the next Mersenne exponent might be about 38,000,000 yielding a Mersenne with about 11.5 million digits. Or it may not." But he then shows graphs that claim M45 is almost certainly between 25 and 27.5 million.

As for the topic of this thread, I don't think a 100 million digit prime will be found before 2020.

Last fiddled with by jinydu on 2008-09-14 at 11:48
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Old 2008-09-14, 12:26   #11
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Default >early next week

Less than 3 hours to 15th in Tokyo,
But it may have already been Next Week?
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