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 2005-09-11, 15:13 #1 jasong     "Jason Goatcher" Mar 2005 5×701 Posts How do I determine the xth-highest 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 4000th-highest 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 2005-09-11 at 15:20
 2005-09-11, 15:18 #2 jinydu     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
 2005-09-11, 15:42 #3 paulunderwood     Sep 2002 Database er0rr 3·1,163 Posts http://primes.utm.edu/primes/search.php gives you many options to refine a search... Last fiddled with by paulunderwood on 2005-09-11 at 15:42
 2005-09-11, 23:28 #4 Numbers     Jun 2005 Near Beetlegeuse 38810 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.
2005-09-11, 23:42   #5
jinydu

Dec 2003
Hopefully Near M48

2×3×293 Posts

Quote:
 Originally Posted by Numbers 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.
He meant the x-th largest known prime, not the x-th prime.

For instance, the first largest known prime is M42.

 2005-09-12, 08:04 #6 Numbers     Jun 2005 Near Beetlegeuse 22×97 Posts Doh.... (we need a smiley in the form of Homer for occasions like this) Last fiddled with by Numbers on 2005-09-12 at 08:05 Reason: mis-spelling
2005-09-12, 12:26   #7
R.D. Silverman

Nov 2003

1C4016 Posts

Quote:
 Originally Posted by jasong I'm surfing [url=http://primes.utm.edu/]
"Is there a method to use if I wanted to find, say, the 4000th-highest prime found?"

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 post-processing suite for my NFS work.
However, I have written my own post-processing 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 prime-hunting 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?

2005-09-13, 20:41   #8
jasong

"Jason Goatcher"
Mar 2005

5·701 Posts

Quote:
 Originally Posted by R.D. Silverman "Is there a method to use if I wanted to find, say, the 4000th-highest prime found?" 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.
That's a good point, although I've found these types of answers annoy most people(I know this because I've given similar type answers in the past)\

Quote:
 Originally Posted by R.D. Silverman "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 post-processing suite for my NFS work. However, I have written my own post-processing 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 prime-hunting 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?
Hard in terms of math, or hard in terms of new experiences? The hardest problem I have in my life is getting a girlfriend, my anxiety disorder has prevented me from doing that since I was seventeen. Achieving that would be preferable to even a top-20 prime.

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