20050911, 15:13  #1 
"Jason Goatcher"
Mar 2005
3507_{10} Posts 
How do I determine the xthhighest prime on prime pages?
I'm surfing this prime site, and I'm trying to determine how to find primes of specific ranks.
Is there a method to use if I wanted to find, say, the 4000thhighest prime found? The reason I ask is that I'm involved in 15k, and it would be nice to be in the top 5000 for six months to a year at least. Can anybody solve my problem, or give any kind of advice? Edit: Okay, I figured it out, the magic number of digits to get above 4000 is 64450. Sorry to clog the forums. Last fiddled with by jasong on 20050911 at 15:20 
20050911, 15:18  #2 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
You can download the complete list of the top 5000 largest known primes here:
http://primes.utm.edu/primes/download.php 
20050911, 15:42  #3 
Sep 2002
Database er0rr
2·5·467 Posts 
Last fiddled with by paulunderwood on 20050911 at 15:42 
20050911, 23:28  #4 
Jun 2005
Near Beetlegeuse
2^{2}·97 Posts 
You can of course also work it out for yourself. The probability that n is prime is approx. 1/Log(n), so the nth prime is approx. n * Log(n).
Approx. means that when n = 10^11 the error is about 8%, which will at least put you in the right ballpark. 
20050911, 23:42  #5  
Dec 2003
Hopefully Near M48
11011011110_{2} Posts 
Quote:
For instance, the first largest known prime is M42. 

20050912, 08:04  #6 
Jun 2005
Near Beetlegeuse
2^{2}×97 Posts 
Doh....
(we need a smiley in the form of Homer for occasions like this) Last fiddled with by Numbers on 20050912 at 08:05 Reason: misspelling 
20050912, 12:26  #7  
"Bob Silverman"
Nov 2003
North of Boston
7558_{10} Posts 
Quote:
The short answer is no. (1) What you seek is a moving target. It changes all the time. (2) A yes answer would be predicated on assuming that all such known primes have been *reported* and furthermore, have been *displayed* in a public website. This can not be assumed. "it would be nice to be in the top 5000 for six months to a year at least." Why? What value does it have? I don't understand what value it would have to you. *IF* you had written the code to find such a prime, then you could be very proud of such a discovery. But blindly running black box code written by others has very little value, at least IMO. It is true that I use the CWI postprocessing suite for my NFS work. However, I have written my own postprocessing code, except for the final square root. I use the CWI suite because it is substantially better. (although my Block Lanczos code is nearly as fast as theirs). I simply do not have the time to optimize all of the code that I have written. They also use a better algorithm for filtering (cliques) than I do (intelligent Gaussian elimination). I would have more respect for your primehunting efforts if you would at least *TRY* to write your own code, even if it is inefficient. Finding large primes is a relatively *easy* problem, because they are abundant. Why don't you try something HARD? 

20050913, 20:41  #8  
"Jason Goatcher"
Mar 2005
3·7·167 Posts 
Quote:
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