20080913, 15:00  #1 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}×3^{2}×13^{2} Posts 
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,

20080913, 16:32  #2 
Apr 2008
Regensburg..^~^..Plzeň
5·17 Posts 
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 20080913 at 16:42 Reason: adjust link 
20080913, 16:40  #3 
Dec 2003
Hopefully Near M48
11011011110_{2} Posts 
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 20080913 at 16:41 
20080913, 17:59  #4  
Apr 2008
Regensburg..^~^..Plzeň
5·17 Posts 
Quote:
nelson Last fiddled with by Nelson on 20080913 at 18:04 Reason: correcting Arithmetic 

20080913, 19:00  #5 
Feb 2004
France
2·457 Posts 
2023
My guess is: 2023.
Tony 
20080913, 21:56  #6 
Apr 2006
Down Under
59_{16} Posts 
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. 
20080914, 02:00  #7 
Einyen
Dec 2003
Denmark
3,037 Posts 
http://v5www.mersenne.org/
If you add the columns LLD + 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 1M10M digit range. I get around 670.000. Then add up the LLERR + NOLL columns from 33,000,000 up to and including 331,000,000 you get approximately the number of LLtest to be done in the 10M100M 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 5860bits. 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 1M10M range. 
20080914, 09:02  #8 
I quite division it
"Chris"
Feb 2005
England
4035_{8} Posts 
My guess is the 2nd half of 2015.

20080914, 10:24  #9 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
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 oneoff escalation in participation. BTW in another list, Chris Caldwell opined that these latest two primes were overdue. I had to disagree with him. David 
20080914, 11:47  #10 
Dec 2003
Hopefully Near M48
3336_{8} Posts 
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 20080914 at 11:48 
20080914, 12:26  #11 
Sep 2008
3 Posts 
>early next week
Less than 3 hours to 15th in Tokyo,
But it may have already been Next Week? 
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