One question about base 3,5,7

[pepi37]

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

[R.D. Silverman]

Originally Posted by pepi37

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

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

[pepi37]

Originally Posted by R.D. Silverman

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

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 :)

[R.D. Silverman]

Originally Posted by pepi37

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 :)

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.

[Mini-Geek]

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 Sierpinski/Riesel Base 5 Project 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: CRUS, Riesel conjectures, Sierp conjectures)

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.

[pepi37]

Originally Posted by R.D. Silverman

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.

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

[pepi37]

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) :))

[Mini-Geek]

Originally Posted by pepi37

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) :))

As far as I know, yes. That particular k is a Williams Sequence, but appears to have been searched to a maximum of 1063844. But in general: pick a k, any k.
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 Open Projects or the CRUS subforum.

[pepi37]

Originally Posted by Mini-Geek

As far as I know, yes. That particular k is a Williams Sequence, but appears to have been searched to a maximum of 1063844. But in general: pick a k, any k.
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 Open Projects or the CRUS subforum.

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 :)