How do I determine the xth-highest prime on prime pages?
 

I'm surfing [url=http://primes.utm.edu/]this prime site[/url], 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.

You can download the complete list of the top 5000 largest known primes here:

[url]http://primes.utm.edu/primes/download.php[/url]

[url]http://primes.utm.edu/primes/search.php[/url]

gives you many options to refine a search... :grin:

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.

[QUOTE=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.[/QUOTE]

He meant the x-th largest known prime, not the x-th prime.

For instance, the first largest known prime is M42.

Doh....

(we need a smiley in the form of Homer for occasions like this)

[QUOTE=jasong]I'm surfing [url=http://primes.utm.edu/]

<snip>

[/QUOTE]

"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?

[QUOTE=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.[/quote]
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="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?[/QUOTE]
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.