About site: Math/Number Theory/Prime Numbers - Entropy and Prime Numbers
Return to Science
  About site: http://web.tiscali.it/GEB/sfteng.htm

Title: Math/Number Theory/Prime Numbers - Entropy and Prime Numbers Entropy of a nonnegative adjacency matrix related to prime numbers.
The_First_5,800,000_Prime_Numbers Site includes known primes k*2^n-1 for k=301 to 999.

Formulae_for_Primes Contains a formula by Jones, Sato, Wada and Wiens. The set of primes is the set of positive values taken by this expression.

Generalized_Fermat_Prime_Search Software, results and other resources.

Generalized_Woodall_Numbers An organized search for primes of the form n*b^n-1.

Hardy-Littlewood_Constants Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.

Henri_Lifchitz Research in number theory, prime numbers and parity of arithmetic functions. Includes primality testing theorems and prime number chains. In English and French.


  Alexa statistic for http://web.tiscali.it/GEB/sfteng.htm





Get your Google PageRank






Please visit: http://web.tiscali.it/GEB/sfteng.htm
  Related sites for http://web.tiscali.it/GEB/sfteng.htm
    Introduction_to_Twin_Primes_and_Brun\'s_Constant An article by Pascal Sebah with the results of computation of the twin primes up to 5.10^15.
    Introductory_Prime_Number_Theory_Resources Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers.
    Jens_Kruse_Andersen Prime constellation records. Arithmetic progressions, simultaneous primes, prime gaps.
    K-Tuple_Permissible_Patterns Findings using an exhaustive search by Thomas J Engelsma.
    MacTutor_History_of_Mathematics__Prime_Numbers Includes biographies on many mathematicians.
    MathWorld__Prime_Numbers Index to hundreds of prime-related articles in Eric Weisstein's MathWorld.
    The_Nine_and_Ten_Primes_Project The discovery of nine and finally ten consecutive primes in arithmetic progression.
    Notes_and_Literature_on_Prime_Numbers With applets to demonstrate properties of primes.
    Number_Spiral Explains this method of visually representing the distribution of primes and the relationships between factors and products.
    On-Line_Encyclopedia_of_Integer_Sequences_(OEIS)__Primes Index to information about many integer sequences involving primes. Site includes numerous other prime-related sequences.
    Patterns_in_Primes Examples of mostly digit patterns collected by Harvey Heinz.
    Primality Introductory text on the theory of prime numbers and number fields. Contains proofs of some important theorems including the fundamental theorem of arithmetic. [PDF]
    Primality_Testing_with_Fermat\'s_Little_Theorem Test numbers for primality and pseudoprimality in Java.
    Prime_k-tuplets Tony Forbes' extensive collection of special types of prime clusters.
    The_Prime_Machine Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
    Prime_Music A musical piece translating prime factorizations to frequencies. Requires RealPlayer.
    Prime_Numbers Short lesson.
    Prime_Numbers_and_Factoring Links and references related to primes and factoring.
    Prime_Numbers_List Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
    The_Prime_Page Methods and definitions of finding prime numbers.
    Radiant_Primes Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
    Some_Prime_Numbers Sieves and factoring for small numbers. Download primes below 8 billion.
    Status_of_Search_for_Multifactorial_Primes An organized search for primes of the form (n)(n-k)(n-2k)...+/-1. Includes table of numbers searched and primes found.
    Thomas_R__Nicely Includes twin prime counts, tables of first occurrence prime gaps, papers.
    The_Time_Traveler A group with new propositions in various areas of number theory.
    Visualizing_the_Distribution_of_Prime_Numbers Investigation into patterns in the distribution of the primes by visualizing them.
    Wikipedia__Prime_Numbers Index to many prime-related articles.
    World_of_Numbers__World_of_Palindromic_Primes Records, statistics, curios and puzzles about primes reading the same backwards. Compiled by Patrick De Geest.
    Bipeds_and_Prime_Numbers Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity. (September 18, 2001)
    Chair_of_General_Chemistry,_Altai_State_Technical_University Describes scientific work and educational programs, lists group publications.
    Department_of_Chemistry Contains online course material and lists faculty members.
    Earth_Measurement_Corp_ Near-surface geophysical data acquisition, processing and interpretation.
    Electro-Seise,_Inc_ 3D airborne micro gravity/E surveys for subsurface hydrocarbons.
    Fairfield_Industries_Incorporated Fairfield is a geophysical company known for its development and use of advanced technology for acquisition and processing, and its licensing of seismic data.
    G_A__Ryzhikov_and_M_S__Biryulina,_Consultants Special processing for traditional marine data using "Partial Synergetic Imaging-", or PSI-criterion.
    Getech Geophysical contractor providing gravity and magnetic services and products to the international oil and mining industry. Offices in Leeds and Houston.
    Gibson_Consulting Interpretation of gravity & magnetics for hydrocarbon exploration.
    Input_Output,_Inc_ Provider of land, marine and reservoir seismic instrumentation. Includes comprehensive data sheets.
    Interactive_Interpretation_&_Training,_Inc_ Outsourcing geoscience for the upstream petroleum industry: geophysics, geology, petroleum engineering, geochemistry, workstation rental. Landmark and GeoQuest software.
    JGI,_Inc_ Acquisition of seismic and other geophysical data, geothermal surveys and remote sensing. Japan based.
This is now2007.com cache of m/ as retrieved on 2008.11.22 now2007.com's cache is the snapshot that we took of the page as we crawled the web. The page may have changed since that time.
chiamato = 0; function relink() { document.onclick=function(evt){ var target; evt=evt||window.event; target=evt.target||evt.srcElement; if(target.nodeName=='A' || target.parentNode.nodeName=='A'){ refresh(); } else if(target.onclick || target.parentNode.onclick){ refresh(); } } } myreg=new RegExp("web\.tiscali\.it","i"); if (!myreg.test("'"+top.location+"'")) { top.location=self.location; } var shortuserdir="GEB"; var bannercode="/banner-tiscali/banner.html"; function rescan() { for (var i=0;iEntropy and prime numbersThis is a little result I found during my work for graduation in Mathematics. I’d like to know your opinion about it, so you can send me an e-mail to carla@x-planet.net. You can also visit my new site: http://www.x-planet.net/. Thank you anyway.An application named sftLet P be the prime numbers set and let P(i) be the n-th prime, P(1) = 2. Let p be a prime consisting of n digits, we want to transform it in another n-digits prime. The process is similar to that used for circular primes and it will be very clear with an example: let p = 1997, now we shift p’s digits one position left to obtain 997u, where u is an unknown digit.We want 997u to be a prime so u must be in the set {1, 3, 7, 9} and in our example the only possibility is u = 3.In general we won’t obtain a unique result, in fact for example starting from 1187 we’ll have 1871, 1873, 1877 and 1879 which are all primes.On the other hand there are primes, such as 8713, for which none of the four possible numbers is prime.Let p be a prime consisting of four digits abcd, let’s consider the following set{bcd1, bcd3, bcd7, bcd9};then we’ll erase the non prime elements from this set and we’ll call N(p) the resulting set.We call sft(p) the application from P to the elements of N(p).In general, being p a n-digits prime, N(p) is given erasing the non prime elements from the set{10 (p mod 10^(n – 1)) + u}.Construction of the adjacency matrix and evaluation of the entropyThe adjacency matrix C[n] of this application for primes up to n-digits is defined by the following rule: the (i, j) element is 1 if we can go from P(i) to P(j) by the application sft(P(i)), else the (i, j) element is 0.Computing the entropy of this matrix gives us an idea of the complexity of the shift space resulting from the application sft.Moreover entropy is an invariant (not complete) under conjugacy for this kind of spaces.Using the Perron-Frobenius theory we can compute the entropy of the matrix C[n], called h(C[n]), defined by the followingh(C[n]) = log L, where L is the largest eigenvalue of C[n]. This computation gives an unexpected result that ish(C[2]) = h(C[3]) = h(C[4]) > 1.4066;the corrisponding Perron eigenvalue is L > 2.5611. This link will show you the sft application by a plot made starting from matrix C[4] in the following way: a point of coordinates (P(i), P(j)) is plotted corrisponding to the matrix elements equal to 1. Moreover we can see the C[4] matrix plotting a point to represent an element equal to 1. This two plots are strangely similar. A stochastic dynamical system Iterating the application sft on the prime number set P we build a dynamical system on this set. To have a realization of such a system we must operate a choice everytime sft(p) contains more then an element. If this choice is completely random we obtain a stochastic dynamical system as we can see from the following realizations: sometimes the orbits stop, for example 52792797 because sft(p) is empty; sometimes the orbits have no regularity and may continue indefinitely, for example 5279279179199199199799739739739339319319319119139137ecc.A deterministic dynamical systemIf we state a way to choice inside the sft(p) set we'll see a completely different behaviour of the system: for example we can assume min(sft(p)) as iteration of p, now we have a deterministic dynamical system .We'll have orbits that stop after a while as27417411411111171171or more interesting orbits which become circular as527927917919919919939931931131191193193193113119...and12232237237137197193193193113119119319319311...In both the above cases the orbits become periodic as they reach the circular prime 9311. Moreover we can say that this two are the only possible behaviours for the points of such a dynamical system because it is a finite deterministic system.The sft graphic contains every dynamical system that can be made by the C[4] matrix.The author is Carla Chicchiero under direction of Prof. P.E. Ricci, University "La Sapienza", Rome.For the theory about shift spaces see D. Lind and B. Marcus, "An Introduction to Symbolic Dynamics and Coding", Cambridge University Press. relink(); setInterval("rescan()", 1000); top.document.title = top.frames[top.frames.length % 2].document.title;
 

Entropy

of

a

nonnegative

adjacency

matrix

related

to

prime

numbers.

http://web.tiscali.it/GEB/sfteng.htm

Entropy and Prime Numbers 2008 November

dvd rental

dvd


Entropy of a nonnegative adjacency matrix related to prime numbers.

Rules

© 2005 Internet Explorer 5+ or Netscape 6+
Recommended Sites: 1. Arts - Business - Computers - Games - Health - Home - Kids and Teens - News - Recreation - Reference - Regional - Science - Shopping - Society - Sports - World Miss Gallery - Top Anime Hentai - DVD rental by mail - Mobile Phone - Advertising - Loan - Homes for Sale - WesternUnion
2008-11-22 08:47:37

Copyright 2005, 2006 by Webmaster
Websites is cool :)