20130509, 12:14  #1 
Dec 2011
After milion nines:)
3^{2}·5^{2}·7 Posts 
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 
20130509, 12:33  #2  
"Bob Silverman"
Nov 2003
North of Boston
7·1,069 Posts 
Quote:
You need to share it. 

20130509, 13:02  #3  
Dec 2011
After milion nines:)
3^{2}×5^{2}×7 Posts 
Quote:
Number like k*3^20000001/+1 or k*5^20000001/+1 or k*7^12000001/+1 where K is from 2 10 Since I search in MEGA range, I will test it only with "right for me "exponents :) 

20130509, 13:47  #4  
"Bob Silverman"
Nov 2003
North of Boston
1D3B_{16} Posts 
Quote:
(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. 

20130509, 14:34  #5 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
1000010110110_{2} Posts 
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 CRUSstyle 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 5keligible 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. Last fiddled with by MiniGeek on 20130509 at 14:37 
20130509, 14:34  #6  
Dec 2011
After milion nines:)
3^{2}·5^{2}·7 Posts 
Quote:
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 

20130509, 14:38  #7 
Dec 2011
After milion nines:)
3^{2}·5^{2}·7 Posts 
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*3^20000001 ( and up) I will be first that do that in human history ( if I understand you correctly) :)) 
20130509, 14:58  #8  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
2·3·23·31 Posts 
Quote:
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. Last fiddled with by MiniGeek on 20130509 at 14:58 

20130509, 16:59  #9  
Dec 2011
After milion nines:)
3^{2}·5^{2}·7 Posts 
Quote:
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 :) Last fiddled with by pepi37 on 20130509 at 17:58 

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