java - sum(1/prime[i]^2) >= 1? -



java - sum(1/prime[i]^2) >= 1? -

while trying devise algorithm, stumbled upon question. it's not homework.

let p_i = array of first primes. need smallest i such that

sum<n=0..i> 1 / (p_i[n]*p_i[n]) >= 1.

(if such i exists).

an approximation i'th prime i*log(i). tried in java:

public static viod main(string args[]) { double sum = 0.0; long = 2; while(sum<1.0) { sum += 1.0 / (i*math.log(i)*i*math.log(i)); i++; } system.out.println(i+": "+sum); }

however above doesn't finish because converges 0.7. 1/100000000^2 rounds 0.0 in java, that's why doesn't work. same reason doesn't work if replace 6th line with

sum += 1.0 / (i*i)

while should reach 1 if i'm not mistaken, because sum should incease faster 1/2^i , latter converges 1. in other words, shows java rounding causes sum not reach 1. think minimum i of problem should exist.

on maths side of question, not java side:

if understand problem, there no solution (no value of i).

for finite set p_i of primes {p_1, p_2,...p_i} allow n_i set of integers p_i, {1,2,3,...,p_i}. sum 1/p^2 (for p_n in p_i) less sum of 1/x^2 x in n_i.

the sum of 1/x^2 tends ~1.65 since 1 never in set of primes, sum limited ~0.65

java algorithm math primes rounding

Comments

Post a Comment

Popular posts from this blog

xslt - DocBook 5 to PDF transform failing with error: "fo:flow" is missing child elements. Required content model: marker* -

xslt - DocBook 5 to PDF transform failing with error: "fo:flow" is missing child elements. Required content model: marker* - i've inherited doc publishing process takes docbook , builds html , pdf output, using apache fop both. project had been started, never completed. lots of tweaking, i've able of doc sets build (20+), except handful, , fail severe code 1 of these 2 conditions: "fo:flow" missing kid elements. required content model: marker* "fo:block" not valid kid of "fo:root" the xml output comes out of docbook , docbook-fop checks out well-formed. the fop error in 1 book, "endecagloss", example, points end of string: <fo:flow flow-name="xsl-region-body" start-indent="4pc" end-indent="0pt"/> here’s log output in case: [java] severe: javax.xml.transform.transformerexception: file:/scratch/publishing/hudson/jobs/build-main-endeca-documentation/workspace/serverdoc/w...
Read more

mediawiki - How do I insert tables inside infoboxes on Wikia pages? -

mediawiki - How do I insert tables inside infoboxes on Wikia pages? - i want insert tables in infoboxes. example, have proteinbox i've developed using infobox template (http://health-and-medicine.wikia.com/wiki/template:proteinbox), , fasta field big fit comfortably in proteinbox. hence collapsible table within box. this tried: {{infobox | row 1 = {| class = "mw-collapsible mw-collapsed wikitable" |- | <!-- table content --> |} }} your problem is, putting nested table within template. pipe characters ( | ) in table syntax collides pipe usage in templates. the commonly used hack around create template called template:! , containing pipe character, , utilize when need set tables, parser functions or other stuff using pipe characters, within templates. table (with every | replaced {{!}} ): {{{!}} {{!}}- {{!}} a1 {{!}} b1 {{!}}- {{!}} a2 {{!}} b2 {{!}}} ...the equivalent of {| |- | a1 | b1 |- | a2 | b2 |} furthermore, hav...
Read more

Local Service User Logged into Windows -

Local Service User Logged into Windows - i created windows service tracks app server user connected through load balancer. it retrieves user logged windows on machine, cross references active directory (ad) business relationship homecoming first name, lastly name , e-mail (for notification through website created project) there 1 scheme on network users remote system, vista system, reason returning values "local service" logged machine, it's weird , security guys impossible "local service" business relationship logged windows. here how user logged windows managementscope ms = new managementscope("\\\\.\\root\\cimv2"); objectquery query = new objectquery("select * win32_computersystem"); managementobjectsearcher searcher = new managementobjectsearcher(ms, query); foreach (managementobject mo in searcher.get()) { _username = mo["username"].tostring(); } // remove domain part username string[] usernameparts = _...
Read more