1. Prime Conjectures And Open Question Another page about Prime Numbers and related topics. Prime conjectures and Open Questions. (Another of the Prime Pages' resources) http://www.utm.edu/research/primes/notes/conjectures

Prime Conjectures and Open Questions (Another of the Prime Pages ' resources Home Search Site Largest Finding ... Submit primes Below are just a few of the many conjectures concerning primes. Goldbach's Conjecture: Every even n Goldbach wrote a letter to Euler in 1742 suggesting that . Euler replied that this is equivalent to this is now know as Goldbach's conjecture. Schnizel showed that Goldbach's conjecture is equivalent to distinct primes It has been proven that every even integer is the sum of at most six primes [ ] (Goldbach's conjecture suggests two) and in 1966 Chen proved every sufficiently large even integers is the sum of a prime plus a number with no more than two prime factors (a P ). In 1993 Sinisalo verified Goldbach's conjecture for all integers less than 4 ]. More recently Jean-Marc Deshouillers, Yannick Saouter and Herman te Riele have verified this up to 10 with the help, of a Cray C90 and various workstations. In July 1998, Joerg Richstein completed a verification to 4

2. F. Conjectures (Math 413, Number Theory) Shop here for conjectures and Refutations The Growth of Scientific Knowledge and find more books by Karl R. Popper. For a limited time, get free shipping on orders over $25! http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem The Riemann Hypothesis Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Conj: The only zeros of Z( s ) are at s s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M n , is defined by M n n Thm: M n is prime implies that n n is perfect. (Euclid)

3. Institutt For Matematiske Fag Summer School 2001 Homological conjectures for finite dimensional algebras August 12th 19th, Nordfjordeid, Norway Addresses, sources of information http://www.math.ntnu.no/~oyvinso/Nordfjordeid

Summer School 2001: Homological conjectures for finite dimensional algebras August 12th - 19th, Nordfjordeid, Norway Announcements Invitation Program for the first part Distribution of lectures in the first part References for the first part ... Unoffical summer school picture Addresses, sources of information Organisers The Sophus Lie conference center Travel information Registration/Participants Participants of the summer school Support Financial Support of Young Researchers Application form The summer school is supported by the European Union, The Research Council of Norway, Nansenfondet og de dermed forbundne fond, The department of mathematical sciences, NTNU. NTNU Fakultet Institutt Teknisk ansvarlig: Webmaster Oppdatert:

4. Conference On Stark's Conjectures For Lecture Notes Click Here Conference on Stark's conjectures and Related Topics Johns Hopkins University, Department of Mathematics August 59, 2002 A conference funded by the National Science Foundation, the Number Theory Foundation and Johns http://www.mathematics.jhu.edu/stark

For Lecture Notes Click Here Conference on Stark's Conjectures and Related Topics Johns Hopkins University, Department of Mathematics August 5-9, 2002 A conference funded by the National Science Foundation, the Number Theory Foundation and Johns Hopkins University. Organizing Committee David Burns , King's College London, UK, david.burns@kcl.ac.uk Cristian Popescu , Johns Hopkins University, USA, cpopescu@math.jhu.edu Jonathan Sands , University of Vermont, USA, sands@math.uvm.edu David Solomon , King's College London, UK, solomon@mth.kcl.ac.uk Description of the conference In the last few years there has been a surge in research activity dedicated towards obtaining further explicit evidence for Stark's Conjecture, and in formulating and investigating natural variants, refinements or generalizations thereof. By bringing together the leading exponents of these different strands of research this conference aims to improve understanding of the links between them. In addition, the conference program will include a series of survey talks aimed at making accessible to as wide an audience as possible the main aspects of recent research into Stark's Conjecture. At this time, confirmed main speakers include.

5. Some Open Problems Open problems and conjectures concerning the determination of properties of families of graphs. http://www.eecs.umich.edu/~qstout/constantques.html

Some Open Problems and Conjectures These problems and conjectures concern the determination of properties of families of graphs. For example, one property of a graph is its domination number. For a graph G , a set S of vertices is a dominating set if every vertex of G is in S or adjacent to a member of S . The domination number of G is the minimum size of a dominating set of G . Determining the domination number of a graph is an NP-complete problem, but can often be done for many graphs encountered in practice. One topic of some interest has been to determine the dominating numbers of grid graphs (meshes), which are just graphs of the form P(n) x P(m) , where P(n) is the path of n vertices. Marilynn Livingston and I showed that for any graph G , the domination number of the family G x P(n) has a closed formula (as a function of n ), which can be found computationally. This appears in M.L. Livingston and Q.F. Stout, ``Constant time computation of minimum dominating sets'', Congresses Numerantium (1994), pp. 116-128. Abstract Paper.ps

6. Conjectures In Geometry conjectures in Geometry. Twenty conjectures in Geometry Vertical AngleConjecture Nonadjacent angles formed by two intersecting lines. http://www.geom.umn.edu/~dwiggins/mainpage.html

Conjectures in Geometry An educational web site created for high school geometry students by Jodi Crane, Linda Stevens, and Dave Wiggins Introduction: This site constitutes our final project for Math 5337-Computational Methods in Elementary Geometry , taken at the University of Minnesota's Geometry Center during Winter of 1996. This course could be entitled "Technology in the Geometry Classroom" as one of its more important objectives is to provide students (presumably math educators) with a wide variety of activities (demonstrations and assignments) utilizing computer software that could be incorporated into a high school geometry classroom. This page has been designed to provide an interactive technological resource for students studying elementary high school geometry. Basic concepts, conjectures, and theorems found in typical geometry texts are introduced, explained, and investigated. Follow-up activities are provided to further demonstrate meanings and applications of concepts. The objective is to ensure that students develop a firm understanding of both the content and applications of each main idea given below in the list of conjectures. Working towards this objective, we have included:

7. Conjectures In Geometry: Parallelogram Conjectures Parallelogram conjectures. Explanation A parallelogram is a quadrilateral withtwo pairs of parallel sides. The precise statement of the conjectures are http://www.geom.umn.edu/~dwiggins/conj22.html

Parallelogram Conjectures Explanation: A parallelogram is a quadrilateral with two pairs of parallel sides. If we extend the sides of the parallelogram in both directions, we now have two parallel lines cut by two parallel transversals. The parallel line conjectures will help us to understand that the opposite angles in a parallelogram are equal in measure. When two parallel lines are cut by a transversal corresponding angles are equal in measure. Also, the vertical angles are equal in measure. Now we need to extend our knowledge to two parallel lines cut by two parallel transversals. We have new pairs of corresponding angles What can be said about the adjacent angles of a parallelogram. Again the parallel line conjectures and linear pairs conjecture can help us. The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary. The precise statement of the conjectures are: Conjecture ( Parallelogram Conjecture I Opposite angles in a parallelogram are congruent. Conjecture ( Parallelogram Conjecture II Adjacent angles in a parallelogram are supplementary.

8. Peter Flach's PhD Thesis PhD thesis of Peter Flach, investigating the `logic of induction' from philosophical and machinelearning Category Society Philosophy Philosophy of Logic Problem of Induction...... Presentations PhD thesis Thesis cover conjectures. An inquiryconcerning the logic of induction. Peter Flach. This thesis gives http://www.cs.bris.ac.uk/~flach/Conjectures/

Bristol CS Index ML group Peter Flach ... Presentations Conjectures An inquiry concerning the logic of induction Peter Flach This thesis gives an account of my investigations into the logical foundations of inductive reasoning. I combine perspectives from philosophy, logic, and artificial intelligence. Summary Introduction and overview Conclusions Table of Contents and PDF/PostScript ... Download all PostScript (compressed tar archive, 780K) PhD defence picture P A Flach Peter.Flach@bristol.ac.uk . Last modified on Friday 20 November 1998 at 15:35. University of Bristol

9. Conjectures -- An Inquiry Concerning The Logic Of Induction Bristol CS Index Research Publications conjectures aninquiry concerning the logic of induction. Peter Flach. Institute http://www.cs.bris.ac.uk/Tools/Reports/Abstracts/1995-flach.html

Bristol CS Index Research Publications Conjectures an inquiry concerning the logic of induction Peter Flach . Institute for Language Technology and Artificial Intelligence, Tilburg, the Netherlands, April 1995. More behind this link Abstract BibTeX entry Other publications by Peter Flach on Machine Learning on Logic Programming on Artificial Intelligence ... Peter.Flach@bristol.ac.uk . Last modified on Tuesday 19 September 2000 at 16:57. University of Bristol

10. Conjectures? 9 Jan 2000 conjectures?, by Cl0ud24. 9 Jan 2000 Re conjectures?, by Guy Brandenburg http://mathforum.com/epigone/geometry-pre-college/quimpwhosnen

a topic from geometry-pre-college Conjectures? post a message on this topic post a message on a new topic 9 Jan 2000 Conjectures? , by Cl0ud24 9 Jan 2000 Re: Conjectures? , by Guy Brandenburg 10 Jan 2000 Re: Conjectures? , by Chris Nicholson The Math Forum

11. Mersenne Primes: History, Theorems And Lists conjectures and Unsolved Problems; See also Where is the next larger Mersenneprime? 5. conjectures and Unsolved Problems. Is there an odd perfect number? http://www.utm.edu/research/primes/mersenne/

/export/home/users/staff/math2/mathMersenne Primes: History, Theorems and Lists Contents: Early History Perfect Numbers and a Few Theorems Table of Known Mersenne Primes The Lucas-Lehmer Test and Recent History ... Conjectures and Unsolved Problems See also Where is the next larger Mersenne prime? and Mersenne heuristics For remote pages on Mersennes see the Prime Links' Mersenne directory Primes: Home Largest Proving How Many? ... Mailing List 1. Early History Many early writers felt that the numbers of the form 2 n -1 were prime for all primes n , but in 1536 Hudalricus Regius showed that 2 -1 = 2047 was not prime (it is 23 89). By 1603 Pietro Cataldi had correctly verified that 2 -1 and 2 -1 were both prime, but then incorrectly stated 2 n -1 was also prime for 23, 29, 31 and 37. In 1640 Fermat showed Cataldi was wrong about 23 and 37; then Euler in 1738 showed Cataldi was also wrong about 29. Sometime later Euler showed Cataldi's assertion about 31 was correct. Enter French monk Marin Mersenne (1588-1648). Mersenne stated in the preface to his Cogitata Physica-Mathematica (1644) that the numbers 2 n -1 were prime for n 31, 67, 127 and 257

12. Euclid's Elements, Book I conjectures ON ORIGINAL COMPOSITION. by Edward Young http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html

Table of contents Definitions Postulates Common Notions Propositions ... Guide to Book I Definitions Definition 1 A point is that which has no part. Definition 2 A line is breadthless length. Definition 3 The ends of a line are points. Definition 4 A straight line is a line which lies evenly with the points on itself. Definition 5 A surface is that which has length and breadth only. Definition 6 The edges of a surface are lines. Definition 7 A plane surface is a surface which lies evenly with the straight lines on itself. Definition 8 A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line. Definition 9 And when the lines containing the angle are straight, the angle is called rectilinear. Definition 10 When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands. Definition 11 An obtuse angle is an angle greater than a right angle.

13. The Prime Puzzles And Problems Connection Problems Puzzles conjectures. 1. Goldbach's Conjecture. 6.- Quantityof primes in a given range Opperman, Brocard Schinzel conjectures? http://www.primepuzzles.net/conjectures/

Conjectures 1.- Goldbach's Conjecture 2.- Chen's Conjecture 3.- Twin Prime's Conjecture 4.- Fermat primes are finite ... primepuzzles.net . All rights reserved.

14. Conjecture 31. The Fermat-Catalan & Beal's Conjectures Problems Puzzles conjectures. Conjecture 31. The FermatCatalan Beal'sconjectures. As a matter of fact this equation generates two conjectures http://www.primepuzzles.net/conjectures/conj_031.htm

Conjectures Conjecture Here we deal with the Diophantine equation x^p + y^q = z^r The Fermat-Catalan Conjecture x^p + y^q = z^r has only a finite As a matter of fact nowadays only 10 solutions are known: (Catalan) The last five solutions were found by The Beal's Conjecture x, y z are not coprimes Two small examples are: BTW, solving this conjecture - or finding a counterxample - has a cash prize of $ ,000 USD. A good starting point to search for the 11th solution and/or the counterexample to Beal 's conjecture, is this web page by Peter Norvig who is Chief of the Computational Sciences Division at the NASA Ames Research Center Questions: 1) Can you find an eleventh solution to x^p + y^q = z^r or demonstrate that there are no more solutions? 2) Can you find a counterexample to the Beal's conjecture? (*) According to p. 383, "Prime Numbers, a computational perspective", , Springer-Verlag, N.Y., 2001, 2nd printing. Other web-references are: http://mathworld.wolfram.com/Fermat-CatalanConjecture.html

15. On Conjectures Of Graffiti Graffiti is a computer program that makes conjectures in mathematics and chemistry. Links to the Category Science Math Geometry...... http://cms.dt.uh.edu/faculty/delavinae/research/wowref.htm

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16. Equal Sums Of Like Powers Regarding equal sums of like powers, compiled by Chen Shuwen.Category Science Math Number Theory Open Problems......Equal Sums of Like Powers. Unsolved Problems and conjectures. The ProuhetTarry-EscottProblem (1851,1910) conjectures by Chen Shuwen (1997-2001) http://member.netease.com/~chin/eslp/unsolve.htm

Equal Sums of Like Powers Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem a k + a k + ... + a n k = b k + b k + ... + b n k k n Is it solvable in integers for any n Ideal solutions are known for n = 1, 2, 3, 4, 5, 6, 7, 8 ,9, 11 and no other integers so far. How to find new solutions for n = 10 and How to find the general solution for n The general solution is known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) only. The complete symmetric solution have been found for ( k = 1, 2, 3, 4 ) How to find a new solution of the type ( k =1, 2, 3, 4, 5, 6, 7, 8 ) How to find non-symmetric ideal solutions of ( k =1, 2, 3, 4, 5, 6, 7, 8 ) and ( k =1, 2, 3, 4, 5, 6, 7, 8, 9 ) How to find a solution chain of the type ( k = 1, 2, 3, 4 ) a a a a a b b b b b c c c c c ( k = 1, 2, 3, 4 ) Solution chains are known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) and ( k = 1, 2, 3, 4, 5 ) so far. Some other open problems are present on Questions by Lander-Parkin-Selfrige (1967) a k + a k + ... + a m k = b k + b k + ... + b n k Is ( k m n ) always solvable when m n k Is it true that ( k m n ) is never solvable when m n k For which k m n such that m n k is ( k m n ) solvable ?

17. Conjectures Investigating Lost Time Hermann Wolf. conjectures about the Paintingsof Andreas Jauss 1997 1998. For the benefit of understanding http://www.jauss.de/com/news.html

Investigating Lost Time Hermann Wolf Conjectures about the Paintings of Andreas Jauss 1997 - 1998 For the benefit of understanding, first an explanation of the desire d presentation by the artist is necessary. Why are the physical measurements of each work the same? Why are the works mounted, or displayed at public showings, the way that they are? Is the selection or the choice of the shown paintings really exchangeable as it looks? Each painting to be hung for exhibition has the same width and height measurements, and because of this uniformity, the artist is able to accumulate and to hang paintings so that they appear as one "block". The artist is able to cover an entire exhibition space with his paintings ensuring the same space distance between the pieces. Various genres of pictures are included within a block and the variety has significance. Cityscapes are mingled with i nterior views of rooms; close-up resemblances to early film stills are mixed with motifs often drawn from various newsmagazines; depictions of travel destinations share sp

18. The Prime Page's Links++: Theory/conjectures Categories in theory conjectures. Goldbach (8) Goldbach's conjecture allprime number conjectures. Resources in theory conjectures. http://primes.utm.edu/links/theory/conjectures/

Links related to Prime Numbers Add Update New Popular Prime number theory if full of onjectures and open problemsin fact much of the research has been driven by just a few of these questions. Top theory : conjectures Categories in theory : conjectures Goldbach Goldbach's conjecture suggests that every even number greater than 2 is the sum of two primes. Riemann The Riemann Hypothesis is perhaps the most central and important of all prime number conjectures. Resources in theory : conjectures Prime Conjectures and Open Questions - A short list of conjectures and open questions related to prime numbers. (Added: 3-Aug-2000 Hits: 1037 Rating: 4.50 Votes: 2) Rate It The abc conjecture - many conjectures could be proven by just proving this one difficult result. This page includes the abc conjecture, generalizations, consequences, tables, bibliography... (Added: 4-Aug-2000 Hits: 823 Rating: 8.00 Votes: 3) Rate It The New Mersenne Conjecture - Table of the Mersenne primes and how the satisfy the New Mersenne Conjecture (Added: 23-Aug-2000 Hits: 411 Rating: 10.00 Votes: 1)

19. The Prime Glossary: Conjecture These results are called conjectures. Some conjectures stand for hundredsof years before they are finally proven (or disproven). http://primes.utm.edu/glossary/page.php?sort=Conjecture

20. Issues & Views: Conjectures And Myths conjectures and myths. An unpopular truth. Reprinted from Issues Views February 25, 2002. It is indeed astounding to see how far http://www.issues-views.com/index.php/sect/23000/article/23029

Tuesday, March 18, 2003 login register Search printable ... Truly telling it like it is Conjectures and myths Africa's ongoing descent A school with a colored memory Where fear rules Yes to voodoo ... The United States of Mexico View Printable Format (Also enter "Subscribe" to receive free Biweekly Updates) Conjectures and myths An unpopular truth It is indeed astounding to see how far some can stretch their imaginations to find "evidence" of white racism. Consider the example of Dr. Ernest Johnson, a psychologist who concludes, from his study of 1,000 Florida tenth-graders, that black teens tend to be angrier than their white peers. Theorizing that this black anger is bred by white America's many racists, Dr. Johnson does not even speculate as to whether it may result, at least in part, from the constant threat of black predators terrorizing their own neighborhoods. Nor does he trace it, even in part, to the fact that scarcely 35 percent of black youngsters currently live in two-parent homes. But if, as Dr. Saunders claims, black hypertension rates implicate white racism, how then are we to interpret suicide rates? By Saunders' logic, the comparative suicide rates of blacks and whites should reveal important information about the relative degrees of stress afflicting members of each race. A disproportionately high incidence of suicide among blacks, for example, would surely be hailed by "civil rights" messiahs as evidence that racism was casting its deadly shadow over the souls of black Americans.

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