When will GIMPS's first prime...
 

...drop off the top 5000 list?

2^1398269-1 was discovered in 1996, and it's currently the 170th largest known prime: [URL]http://primes.utm.edu/primes/lists/all.txt[/URL]

Any guesses as to when it'll no longer be one of the top 5000 primes? I'll go with August 22, 2017.

170 / 5000 .... Hmmm

I'll guess: "Not in any of our lifetimes".

[QUOTE=Bottom Quark;240982]...drop off the top 5000 list?

2^1398269-1 was discovered in 1996, and it's currently the 170th largest known prime: [URL]http://primes.utm.edu/primes/lists/all.txt[/URL]

Any guesses as to when it'll no longer be one of the top 5000 primes? I'll go with August 22, 2017.[/QUOTE]

Like petrw1 said (5000/170)*14 = about 411-412 years so at the rate it's going some time in about 2407-2408 if I do the math correct.

[QUOTE=petrw1;240983]170 / 5000 .... Hmmm

I'll guess: "Not in any of our lifetimes".[/QUOTE]

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 5-8 years.

EDIT:- But it will still stay in the "special" list a little longer because it is an archivable prime ([url]http://primes.utm.edu/top20/page.php?id=4[/url]). It will drop off from that list once GIMPS has found 8 more primes.

The primes drop off a lot faster after postion #500 or so. This prime:

[URL]http://primes.utm.edu/primes/page.php?id=64332[/URL]

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:
[URL]http://primes.utm.edu/top20/trends.php[/URL]

I don't have time to do that now, so I'll eyeball it and make a guess of October 20, 2016.

Here's another one: [url]http://primes.utm.edu/primes/page.php?id=46[/url]

Entered the list in mid 2001 @ #13. Nine years later, currently at #4000-and-change.

[QUOTE=axn;240987]It will drop off from that list once GIMPS has found 8 more primes.[/QUOTE]

When is Hell supposed to freeze over?

David

[QUOTE=davieddy;240992]When is Hell supposed to freeze over?

David[/QUOTE]

Somewhere around here: [url]http://en.wikipedia.org/wiki/Heat_death_of_the_universe#Timeframe_for_heat_death[/url]

But I'm sure GIMPS will find the needed 8 before that.

[QUOTE=davieddy;240992]When is Hell supposed to freeze over?

David[/QUOTE]Oh no, not again. I had to enlighten _HRB_ about this matter not so long ago.

According to both the best tourist guides ([URL]http://en.wikipedia.org/wiki/Inferno_%28novel%29[/URL] and [URL]http://en.wikipedia.org/wiki/Inferno_%28Dante%29[/URL]) it has already partially frozen over.

Paul

[QUOTE=axn;240987]It will drop off from that list once GIMPS has found 8 more primes.[/QUOTE]

Hmm. [TEX]8e^{-\gamma}\approx4.49[/TEX], 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.

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.