20101209, 19:18  #1 
Dec 2010
2×3^{2} Posts 
When will GIMPS's first prime...
...drop off the top 5000 list?
2^13982691 was discovered in 1996, and it's currently the 170th largest known prime: http://primes.utm.edu/primes/lists/all.txt Any guesses as to when it'll no longer be one of the top 5000 primes? I'll go with August 22, 2017. Last fiddled with by Bottom Quark on 20101209 at 19:21 
20101209, 19:28  #2 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
10D8_{16} Posts 
170 / 5000 .... Hmmm
I'll guess: "Not in any of our lifetimes". 
20101209, 19:41  #3  
"Forget I exist"
Jul 2009
Dumbassville
8384_{10} Posts 
Quote:


20101209, 19:54  #4 
Jun 2003
1001000010110_{2} Posts 
I beg to differ. 1.4MBits is not that difficult to overhaul. PrimeGrid's Proth Prime Search alone has the potential to kick this off the list in about 58 years.
EDIT: But it will still stay in the "special" list a little longer because it is an archivable prime (http://primes.utm.edu/top20/page.php?id=4). It will drop off from that list once GIMPS has found 8 more primes. Last fiddled with by axn on 20101209 at 19:57 
20101209, 19:56  #5 
May 2010
499 Posts 
The primes drop off a lot faster after postion #500 or so. This prime:
http://primes.utm.edu/primes/page.php?id=64332 had a rank of 481 in April 2003, but fell of the list in June 2006. One way of guessing would be to fit a regression line to this data: http://primes.utm.edu/top20/trends.php I don't have time to do that now, so I'll eyeball it and make a guess of October 20, 2016. 
20101209, 20:23  #6 
Jun 2003
4630_{10} Posts 
Here's another one: http://primes.utm.edu/primes/page.php?id=46
Entered the list in mid 2001 @ #13. Nine years later, currently at #4000andchange. 
20101209, 20:36  #7 
"Lucan"
Dec 2006
England
6474_{10} Posts 

20101209, 20:58  #8 
Jun 2003
1216_{16} Posts 
Somewhere around here: http://en.wikipedia.org/wiki/Heat_de...for_heat_death
But I'm sure GIMPS will find the needed 8 before that. 
20101209, 21:11  #9 
Bamboozled!
May 2003
Down not across
2^{4}×17×37 Posts 
Oh no, not again. I had to enlighten _HRB_ about this matter not so long ago.
According to both the best tourist guides (http://en.wikipedia.org/wiki/Inferno_%28novel%29 and http://en.wikipedia.org/wiki/Inferno_%28Dante%29) it has already partially frozen over. Paul 
20101209, 21:14  #10 
Aug 2006
5862_{10} Posts 
Hmm. , and two to that power is about 22.5, so that's expected to occur when we're working with Mersenne exponents about 22.5 times larger. If we're around 30 million right now, that would be 675 million.
Assuming (for simplicity) that the work needed to test an exponent is proportional to the square of the exponent and that all prime exponents are tested, that would require about 10,000 times the total effort of GIMPS to date. If half of that effort happened in the past two years, and GIMPS' computing power doubles every two years (by some combination of Moore's law and recruitment), this would require 2 lg(ln(2) * 20,001) or 27.5 years. Assuming instead that it doubles every two years for a decade and then holds constant, it would take about 2 * 20000/2^5 + 10 = 1260 years. So the timeline depends strongly on the assumptions made. Last fiddled with by CRGreathouse on 20101209 at 21:20 
20101209, 21:31  #11 
May 2004
New York City
1083_{16} Posts 
I'll venture to say it won't be within one year, and so
interpolating "not in our lifetimes" and "one year" I get an estimate of "more than two years". And frozen hells will never happen. 
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