One question about base 3,5,7
 

I do search on Prime 5000 list for primes with little K for base 3,5,7 and found only few ones.
It must be simple answer why noone search in those ranges, but it looks like I miss point :(

Or just noone is not interested in those ranges?

Thanks for answers

[QUOTE=pepi37;339815]I do search on Prime 5000 list for primes with little K for base 3,5,7 and found only few ones.
It must be simple answer why noone search in those ranges, but it looks like I miss point :(

Or just noone is not interested in those ranges?

Thanks for answers[/QUOTE]

Define 'little K'. Define 'base'. You obviously have some notation in mind.
You need to share it.

[QUOTE=R.D. Silverman;339816]Define 'little K'. Define 'base'. You obviously have some notation in mind.
You need to share it.[/QUOTE]


Number like k*3^2000000-1/+1 or k*5^2000000-1/+1 or k*7^1200000-1/+1 where K is from 2- 10
Since I search in MEGA range, I will test it only with "right for me "exponents :)

[QUOTE=pepi37;339818]Number like k*3^2000000-1/+1 or k*5^2000000-1/+1 or k*7^1200000-1/+1 where K is from 2- 10
Since I search in MEGA range, I will test it only with "right for me "exponents :)[/QUOTE]

Thanks for the quick reply. There are two possibilities:

(1) The ranges have already been searched and nothing was found.
(2) Total CPU resources are finite and people have been working on other things.

The only searches I know of on those bases are attempting to prove the Riesel and Sierpinski (Sierp) conjectures for them. Bases 3 and 7 have VERY high conjectured k's, and since ranges are typically searched in ascending values of n, top 5000 results aren't likely for these. Base 5 is searched by the [URL="http://www.primegrid.com/forum_thread.php?id=3008&nowrap=true#30725"]Sierpinski/Riesel Base 5 Project[/URL] and produces new primes on the top 5000 list now and then; due to the nature of CRUS-style searches, however, these will be sparse. (more links: [URL="http://www.noprimeleftbehind.net/crus/"]CRUS[/URL], [URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm"]Riesel conjectures[/URL], [URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm"]Sierp conjectures[/URL])

Ultimately, the answer to "why aren't there many top 5000 primes for bases 3, 5, and 7" is that "there's not much effort being put to search for these primes". Base 2 is more efficient to search than other bases, at least up to a certain k (large k's reduce efficiency). If you're simply interested in finding lots of top 5k-eligible primes, k*2^n+-1 is the most efficient choice, which is why so much effort is directed towards it, which is why it's the most common thing on the top 5k list.

[QUOTE=R.D. Silverman;339821]Thanks for the quick reply. There are two possibilities:

(1) The ranges have already been searched and nothing was found.
(2) Total CPU resources are finite and people have been working on other things.[/QUOTE]

It looks impossible (to me) that there is no prime in range K=2-10 base 3 for example below N=2.3M
Something is fishy here :)
For example base 10 have fairly big number ( biggest is around 800000 digits) but only few are reported ...
So second option look realistic

Mini Geek, thanks for answer.
I found to be problem reserve any riesel in relatively lower K ( below 100) because many users do search in that range.
So if I start to search prime in lets say 2*3^2000000-1 ( and up) I will be first that do that in human history ( if I understand you correctly) :))

[QUOTE=pepi37;339826]Mini Geek, thanks for answer.
I found to be problem reserve any riesel in relatively lower K ( below 100) because many users do search in that range.
So if I start to search prime in lets say 2*3^2000000-1 ( and up) I will be first that do that in human history ( if I understand you correctly) :))[/QUOTE]

As far as I know, yes. That particular k is a [URL="http://oeis.org/A003307"]Williams Sequence[/URL], but appears to have been searched to a maximum of 1063844. But in general: pick a k, any k. :smile:
I don't know of anyone keeping reservations on such ranges, so if you decide to work such a range, you might want to announce it as a reservation somewhere, maybe [URL="http://www.mersenneforum.org/forumdisplay.php?f=80"]Open Projects[/URL] or the [URL="http://www.mersenneforum.org/forumdisplay.php?f=81"]CRUS subforum[/URL].

[QUOTE=Mini-Geek;339829]As far as I know, yes. That particular k is a [URL="http://oeis.org/A003307"]Williams Sequence[/URL], but appears to have been searched to a maximum of 1063844. But in general: pick a k, any k. :smile:
I don't know of anyone keeping reservations on such ranges, so if you decide to work such a range, you might want to announce it as a reservation somewhere, maybe [URL="http://www.mersenneforum.org/forumdisplay.php?f=80"]Open Projects[/URL] or the [URL="http://www.mersenneforum.org/forumdisplay.php?f=81"]CRUS subforum[/URL].[/QUOTE]

I must lower k as possible since higher K give me more FFT length, and more length give mu longer computation time....
So 2 for k is not bad choice, and also in range of mega/near mega is not searched...
Batch of new possibilities are now open :)
I made small initial sieve, and it looks like sieve for those exponents are HUGE ( aprox~ 600kb for range of 1M)
If use small range then it is bigger chance to miss prime, and if I use large range will take too long to compute...
I must or leave idea, or make progress in small steps :)