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         Perfect And Prime Numbers:     more detail
  1. Perfect Numbers: Perfect Number, Mersenne Prime, 6, 28, List of Perfect Numbers, 496
  2. Integer Sequences: Prime Number, Factorial, Binomial Coefficient, Perfect Number, Carmichael Number, Integer Sequence, Mersenne Prime
  3. Geometric and Analytic Number Theory (Universitext) by Edmund Hlawka, Johannes Schoißengeier, et all 1991-08-23

1. Algebraic.net - Theorems_And_Conjectures: Perfect And Prime Numbers
Techangel Forums Powered By XMB 1.8 techangel forums programming perfect and prime numbers, AuthorSubject perfect and prime numbers. mrplow Administrator
http://www.algebraic.net/theorems_and_conjectures/perfect_and_prime_numbers.html

2. Number Theory
proof with perfect and prime numbers Use this control to limit the display of threads to those newer than the
http://www.mathhelpforum.com/math-help/f7/i3.html

3. MATHEMATICAL CONCEPTS AS TOOLS IN APPLICATION TO COMPUTING
of numerical functions can be utilized in other situations generating numbers with special properties like Pythagorean triples, abundant, deficient, perfect and prime numbers
http://www2.potsdam.edu/abramovs/Conceptsastools.doc
<J^TpPWd~㧬

4. Links To Other Sites
Largest Known The largest known Perfect and Prime numbers. Life and numbers of Fibonacci. List of Perfect Numbers. Mathematicians born in Bristol. Math Forum
http://brisray.com/links.htm

5. Algebraic.Net - Theorems And Conjectures: INDEX
Perfect And Prime Numbers (97 sites) Riemann Hypothesis (85 sites) Russell's Paradox (96 sites) Theorem Of Pythagoras (100 sites) Traveling Salesman Problem (93 sites)
http://www.algebraic.net/theorems_and_conjectures/index.html
Algebraic.net Home Theorems And Conjectures : INDEX - (35 SUBJECTS)

6. Perfect And Prime Numbers
I have an assignment that requires one to enter an integer, and then have the program say if it's either a prime number, or a perfect number, and it
http://cboard.cprogramming.com/cplusplus-programming/120834-perfect-prime-number

7. The Discursive Construction Of Cognitive Mechanisms
One could use these numbers in quite a few ways without ever becoming aware of the distinctions between, and the properties of, odd and even, perfect and prime numbers.
http://www.massey.ac.nz/~alock/webdck/webdck.htm
Against cognitivism: the discursive construction of cognitive mechanisms
Andrew Lock
Massey University
Preamble This paper is a first attempt to grapple with this `bit-of-a-problem'. How are humans able to do what they do? That is, have any discourses at all?
Commonalities in Constructive Processes
Fortunately, there are some fundamental compatibilities between the social construction and evolutionary perspectives. The major one of these is that both approaches are concerned to account for processes of construction. Second, they are similar in that they posit ordering principles to the temporal course of construction. The main point made here is that discourses at one point in time have implications that come to be made explicit and thus found new discourses at a later point in time. This is analogous to the evolutionary situation in which biological processes also act to explicate in the future the implications of existing systems. Again, the same situation holds in the historical elaboration of certain symbol systems. In this conceptualisation, the implications of a system at one point serve to specify the possibilities for its future specification and elaboration (I have unpacked this conceptualisation in earlier publications (e.g., 1985, 1986), but these are not yet available here). A concrete example will have to suffice at present. The sequence of symbols that denote natural numbers is a human construction. Now, it is possible to do some quite complex tasks without any abstract conception of number: by `tallying', for example, a shepherd can keep track of his or her flock - mark them out in the morning and tick them home in the evening. If, by any chance, one abstracted numbers out of this practice and expressed them on base 10 with Arabic numerals, then one would get the sequence 1 2 3 4 5 6 7 8 9. One could use these numbers in quite a few ways without ever becoming aware of the distinctions between, and the properties of, odd and even, perfect and prime numbers. One might come to apprehend these distinctions, but then be oblivious to such properties as Goldbach's conjecture: that every even number is the sum of two primes (this conjecture fits every known case, but no proof of it has yet been formulated).

8. Cobblestone&Cricket: A Teacher's Guide To Magic In Math
Discover Pythagoras's secret history of friendly, perfect, and prime numbers. Then grab some scissors and prove Pythagoras was right about right triangles.
http://www.cobblestonepub.com/resources/ody0210t.html
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Ancient China, If I Were a Kid in
If YOU were a kid in the ancient world, everything would be different - or WOULD it?
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Hardcover - $17.95
Teacher's Guide for ODYSSEY TM Magic in Math
Format:
Article / Page
Summary
Skills
"The Puzzling Business of Sam Loyd and Enro Rubik," pg. 6
  • The Fifteen Square of the 1800s and the Rubik's Cube of the 1980s captivated with their unique brands of wizardry. The puzzle masters who invented these "toys" are profiled briefly, and Web sites direct interested "gamers" to find out more. Invention, Logic
"Number Secrets" (Activity), pg. 10
  • Discover Pythagoras's secret history of friendly, perfect, and prime numbers. Then grab some scissors and prove Pythagoras was right about right triangles. Vocabulary, Following Directions
"What's So Magical About Magic Squares?" pg. 13
  • Magic squares may seem like mathematical madness, but anyone who knows the rules can produce them. Explore the history of this ancient pastime and discover the shortcuts that make constructing them a little less magical. Vocabulary, Deductive Reasoning

9. Table Of Contents
Simple applications based on arithmetic operations will include the determination of all factors of a positive integer and the subsequent identification of perfect and prime numbers.
http://www.fbeedle.com/bjp/67-8toc.pdf

10. Defiitionof Perfect Numbers In Math. A Perfect Number Is Any Number That...
Theorem connecting perfect and prime numbers. Examples of perfect numbers. 6 The divisors of 6 are 1,2,3 6. To show that
http://www.mathwarehouse.com/dictionary/P-words/definition-of-perfect-numbers.ph

11. Pythagoras And The Pythagorean Theorem
Studies involving Perfect and Prime Numbers ; Irrational Numbers ; Various theorems/ideas about triangles, parallel lines, circles, etc. Of course THE PYTHAGOREAN THEOREM
http://www.slideshare.net/acavis/pythagoras-and-the-pythagorean-theorem

12. Perfect-Key
Continue the sequences indefinitely in the chart to reveal all Perfect and Prime numbers. Instead of putting every positive integer into Euclid’s theorem 2 n1 (2 n-1) to find the
http://www.borderschess.org/Perfect-Key.htm
Perfect Number Solution Key
n:=1 n:=2 n:=3 n:=4 n:=5 n:=6 n:=7 n:=8 n:=9 a(n) b(n) c(n) f(n) g(n) Prime numbers (cyan background). Perfect numbers (yellow background). The product sequence algorithm of c(n) is the solution key to unlocking all Prime numbers (shaded cyan) and Perfect numbers (shaded yellow) for numbers greater than 6 in our number system. The idea for the algorithm comes from my article: "Prime Consideration for the Perfect Number" shown below. The n sequence (n:=1, n:=2, .. , n:=9) can be easily increased and iterated in a software program. Results for the n sequence, shown in the chart above, were derived from MathCad Professional and Mathematica computer programs. If f(n) is prime, then b(n) is perfect. Also, if f(n) is prime, it will be a Mersenne prime. There are various ways to check a number for primeness. Factoring f(n) can be very slow on extremely large numbers. Using the IsPrime function (Mathcad) or PrimeQ function (Mathematica) takes much less time but gives a probability that a number is Prime. Use of IsPrime or PrimeQ may need to be verified on very large numbers by an independent source. Check out GIMPS (The Great Internet Mersenne Prime Search) at http://www.mersenne.org/prime.htm

13. Edinburgh Geologist -Autumn 2004 Editorial
Euler is, of course, known for his work on perfect and prime numbers. A hundred years later, in 1843, Richard Owen, the Lancastrian palaeontologist, coined the word Dinosaur from
http://www.edinburghgeolsoc.org/edingeologist/z_43_01.html
E dinburgh
G eological
S ociety From here, you can look at the Contents Page for this issue, look at other Editorials or look at the index to all issues T he E dinburgh G eologist - I ssue no 43 - A utumn 2004 Editorial by Alan Fyfe This issue sees a minor change in format, but one which you cannot have failed to have noticed. Council has agreed that, starting with this issue, The Edinburgh Geologist will be published with a colour cover. We tried this for the Silver Anniversary issue and it was voted as a desirable development. Issue number 43... what can I make of that? Well, mathematically, 43 is a prime number and, by coincidence, it was in 1743 that Leonhard Euler was chosen to be director of mathematics in the Berlin Academy when it was founded in the following year. Euler is, of course, known for his work on perfect and prime numbers.
I was sent an article by Helen Smailes, not an article for this magazine, nor even written by Helen, but words written in 1857 for The Scotsman, by someone who signed themselves J.N. The article described a visit to Leadhills. I have reprinted the geological part of the article and added a few editorial comments to put readers in the picture concerning geological thinking of the day. The Scottish Stone Liaison Group (SSLG) sends me a Newsletter from time to time. There has been an interesting discussion on renewed interest in Scottish slate and I thought that readers might be interested in progress. Alan McKinney of the SSLG has brought together extracts from the Newsletters and they are published here.

14. Number Theory [Archive] - Math Help Forum
proof with perfect and prime numbers; proof pentagonal numbers; Binet's formula; Sets of integers, different sums SOLVED Can someone help with a proof involving Euler's phi function?
http://www.mathhelpforum.com/math-help/archive/f-7.html
Math Help Forum University Math Help PDA View Full Version : Number theory
Pages :
  • Units digit of m^5 - m is 0 Legendre Symbol Please critique possible proof of Fermat's Last Theorem Addition of numbers relatively prime ... Some modular arithmetic [SOLVED] number exponentiation Modular multiplicative inverse Questions about Fermat numbers? [SOLVED] Least common multiple - Greatest common divisor Proof of congruence result. Find all values of X that satisfy multiple congruences Proof... please help. ... Six digit perfect squares with all digits even. [SOLVED] Is there a fast way to solve this system of congruences on paper? Convolution Question [SOLVED] Diophantine equation question [SOLVED] Simple Factoring Problem Primes Calculate hugh mod Multiplicative Question ... Congruence Problems [SOLVED] Proof that x^2 = 1 implies x = 1 or x = -1 Integers to the the n-th power Divisible integers Remainders ... How do you prove that p, q and r must be perfect squares? [SOLVED] CRT Proof help Primes from a pattern Remainders mod x size(mn) proof ... Associates and their Norms - Should be easy [SOLVED] Infinitely many primes in Q[Sqrt(d)] Equation Carmichael Number Question Euler's Theorem Questions ... Deduce this result from the Prime Number Theorem [SOLVED] Help with a problem involving the GCD, LCM.

    • 15. SOAR Spring 2003 Course (All About Numbers)
    Week Five Perfect and Prime Numbers; the RSA Algorithm. Most of today was taken up discussing perfect numbers. We say that a number is perfect if it is the sum of all its proper
    http://www.math.toronto.edu/mathnet/SOAR2003/Spring/
    All About Numbers
    About The Course
    This is a course offered through the University of Toronto Department of Mathematics for mathematically interested and capable high school students, particularly those in grades 10 and 11. See the announcement for details, or you may browse week-by-week details that will be posted below. You may also contact the instructor Peter M. Garfield The last meeting of this class was Wednesday, May 28th. Please check the MathNet home page for future SOAR courses.
    Week By Week Class Summaries
    Week Thirteen: A Finale of Unsolved Problems
    We finished the course with a discussion of some open problems in number theory. Rather than go into the actual problems we covered, I will instead just refer you to the bibliography for some interesting web pages. Thanks everyone for wonderful semester! If you didn't fill out the survey , please do so as soon as you can. Thanks. There is no homework this week.
    Week Twelve: A Brief Introduction to Elliptic Curves
    Today's group of the day is that most unusual group of points on an elliptic curve. We usually dealt with curves of the form y =x + ax + b (although we sometimes allow an x term as well). The group operation is, roughly speaking, as follows: two add the points

    16. Educational Web Sites
    fractals, probability, etc.), math help desk (calculators, dictionaries, formulas, games, etc.), famous theorems (Axiom of Choice, Riemann Hypothesis, perfect and prime numbers
    http://download.intel.com/education/common/en/resources/eo/course_resources/Sear
    Educational Web Sites Grade Levels: Elementary School - K-6 Specifically for Grades Pre-K to 3 Specifically for Upper Elementary Grades Middle School ... High School Educational Resource and Reference Sites: Encyclopedias, Dictionaries, Maps, etc. Educational Portals - Collection of Links to All Subject Areas Subject Areas: Art English as a Second Language Geography Health ... World Language - Resources for a variety of foreign languages French German Spanish Elementary School - Grades K-6 Ask Dr. Math Look up math questions and answers or submit your own question. Questions are categorized into grade levels (elementary, middle, high school, and college). Enchanted Learning Resources, crafts, printouts, activities, research information for students, and much more. About.com: Free School Fonts Fonts mimic the style of type used to teach print and cursive handwriting skills. Each link goes to a larger sample, author and description info, and download link. FunBrain Educational games and quizzes for students K-8. Teachers can create and give their own or ready-made quizzes online . I Know That Fun, educational activities across all subjects for kids age 2-12 in an engaging, interactive multimedia environment. Free trial and sample activities; subscription for full-site access and CD-ROM.

    17. Prime Numbers - Page 2
    Perfect and Prime numbers taggrath C++ Programming 3 1022-2009 0213 AM Finding Prime Numbers dan724 C Programming 11 12-14-2008 1212 PM Checking very large prime numbers
    http://cboard.cprogramming.com/c-programming/124773-prime-numbers-2.html

    18. Essentials Online Course
    Free Blogs with No Advertising. Aeonity Blog * With Aeonity Blog you are able to add a photo, create your own free blog designs, or you may use one of their free blog themes—with
    http://download.intel.com/education/Common/en/Resources/EO/Resources/resources.h
    Resources Collaboration
    Collaboration back to top
    Blog Sites Free Blogs with No Advertising Aeonity Blog * With Aeonity Blog you are able to add a photo, create your own free blog designs, or you may use one of their free blog themeswith very artistic backgrounds. Very clean looking blog. All members have their own personal blog rss, for easy syndication to other Web sites. Blogs can be private or public. Blogs/user accounts will be removed if your blog is inactive for more than 3 months. Maximum of 25 images. No formatting of text unless you use BB Code Blogger
    Control who can view and contribute to your blog. Customizable templates and drag-and-drop system lets you easily decide how your page will look and exactly where your posts, profiles, archives and other parts of your blog should live on the page. Create an account, name your blog, choose a template, and start blogging. Edublogs
    Free blogs for teachers, trainers, lecturers, librarians and other education professionals; also comes with a free wiki space. Templates and easy-to-use formatting. Create your own ad-free, fully-featured WordPress blog. Upload up to 25MB of images, audio, documents, presentations, or other digital material you want to share. Choose from over 60 different themes. Complete control over comments, choices about the number of posts to display on your front page and in your feed, profiles, plugins to get your Web stats, multi-user and group blogging simply done through the use of the Users area and more.

    19. QBasic - Number Series, Bases & Manipulation
    Largest Known The largest known Perfect and Prime numbers. Life and numbers of Fibonacci. List of Perfect Numbers. Maths History. Pascal's Triangle and its Patterns
    http://brisray.com/qbasic/qnumber.htm
    HomePage Optical Illusions War Stories QBasic ... Mouse Numbers SeqNo SIRDS Sorts Text ... DLoads " Well, if I called the wrong number, why did you answer? " James Thurber, New Yorker, June 5th 1937. PI :- For example using DIM PI AS SINGLE
    PI = ATN(1) * 4 will give PI as 3.141593, using DIM PI AS DOUBLE
    PI = ATN(1) * 4 will give PI as 3.141592653589793 nth Roots :- 'nRoot.bas Ray Thomas April 2002 'The nth root of a number is the number raised to the (1/n) power: DIM Num AS DOUBLE DIM Root AS DOUBLE DIM Count AS INTEGER CLS PRINT INPUT "Please input the number you want the roots of"; Num PRINT PRINT " n", " nth root", , " nth root ^ n" PRINT FOR Count = 1 TO 10 Root = Num ^ (1 / Count) PRINT Count, Root, Root ^ Count NEXT Count END Number Bases :- Q: Why do mathematicians often confuse Halloween and Christmas?
    A: Because Oct 31 = Dec 25 ... X , X , X , X , X , X , X , X , X , X , X Any number to the power of is 1, any number to the power of 1 is that number. For Base 3 the powers are :- To change a number in a Base back to decimal we once again write the powers of that base and write the number beneath it. We then can then count off the number as a decimal.

    20. On The Recent Origin Of Language
    One could use these numbers in quite a few ways without ever becoming aware of the distinctions between, and the properties of, odd and even, perfect and prime numbers.
    http://www.massey.ac.nz/~alock/webdck/origin.htm
    On the recent origin of symbolically-mediated language and its implications for psychological science.
    Draft chapter prepared for
    S. Lea and M. Corballis (Eds) Evolution of the Hominid Mind
    Oxford: Oxford University Press.
    First draft: February 1997
    Andrew Lock
    Department of Psychology
    Massey University
    Palmerston North
    New Zealand
    A.J.Lock@massey.ac.nz
    www/massey.ac.nz/~ALock Language Origins Typically modern human practices are indexed in the archaeological record from about 40,000 years ago (see below). A number of writers have argued that these practices would not have been possible without the existence of a complex form of linguistic communication (e.g., Davidson and Noble, 1989; Mellars, 1989; Noble and Davidson, 1996). But, do the origins of language pre-date, coincide with, or post-date the transition to these practices? The literature provides hypotheses of all shades. For example, given the evidence for complex artifacts and cultural traditions, 'the first traces of language could have appeared as early as Australopithecus africanus . ... It is easy to imagine some form of language contributing to [the success of Homo erectus ]' (Pinker, 1994: 352-3) (see also Holloway, 1969, and Tobias, 1987, 1991, who argue for an early emergence of language, not with australopithecines, but perhaps with

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