41. Page 015 two primes, Kexue Tongbao 17 (1966), 385386. In this paper, Jing Run Chen stateshis famous theorem saying that both Goldbach's conjecture and the twin prime http://www.math.utoledo.edu/~jevard/Page015.htm

Almost twin primes and Chen's theorem Page maintained by Jean-Claude Evard. Last update: August 7, 2002. Mathematics subject classification numbers: 11P32: Goldbach type theorems and 11N36: Applications of sieve methods Mathematical Review Copies of reviews from Mathematical Review cannot be posted on Web pages, but they can be seen through links to MathSciNet. These links work only in the networks of institutions or on the computers of users who are current subscribers to MathSciNet.. Definitions 1. We say that an integer greater than 1 is an r-almost prime if and only if it is the product of at most r primes. 2. The set of all r-almost primes is denoted by P r 3. We say that a positive integer is an almost prime if and only if it is a 2-almost prime 4. We say that a pair of positive integers are r-almost twin primes if and only if one integer of the pair is a prime and the other is an r-almost prime. 5. We say that a pair of positive integers are almost twin primes if and only if they are 2-almost twin primes Historical result about twin primes and almost twin primes: Chen's theorem

42. Twin Prime Conjecture twin Prime conjecture. The twin Prime conjecture states that thereare an infinite number of twin primes. A twin prime is defined http://www.users.globalnet.co.uk/~perry/maths/twinprimeconjecture/twinprimeconje

Twin Prime conjecture [Home] [Other Maths] Twin Prime conjecture The Twin Prime conjecture states that there are an infinite number of twin primes. A twin prime is defined as a pair of numbers, 6k-1 and 6k+1, such that both are prime. Proof i.e. the TPC is equivalent to the conjecture that there are an infinite number of integers with only even anti-divisors. As 3 as an anti-divisor leaves only multiples of 3 as a candidate, then we only need consider prime anti-divisors greater than or equal to 5. We only need consider prime anti-divisors, as numbers with odd composite anti-divisors also have the prime factors of these composites as anti-divisors. A number with an odd anti-divisor can be written as kp+(p-1)/2 or as kp+(p+1)/2. But we only need to consider integers 0mod3, and this allows us to eliminate some possibilities. To do this, consider the two forms of primes, 6k-1 and 6k+1. Note that these are not twin primes, but that all primes after 3 are of one of these forms. If we look at 6k-1, then the integers we can create are j(6k-1) + 3k - 1 and j(6k-1) + 3k. In both of these cases, if j=1mod3, then neither are divisible by 3, and so we can ignore these possibilites.

43. Twin Prime Conjecture Proof The six wide array further helps to demonstrate the otherwise still unproven conjecturethat there must be infinitely many twin primes, that is, pairs of http://www.recoveredscience.com/primes1ebook02.htm

recoveredscience .com We offer surprises about in our e-book Prime Passages to Paradise by H. PeterAleff Site Contents PRIME PATTERNS Table of Contents Rectangular arrays Twin prime proof Prime facts Prime problems Polygonal numbers Number pyramids ... Reader responses Visit our Sections: Constants Board Games Astronomy Medicine Store Stuff Home Page Search this site FAQ about e-books Download free e-books ... email us Footnotes : Paulo Ribenboim: "The New Book of Prime Number Records", Springer- Verlag, New York, 1996, pages 20 to 52. Calvin C. Clawson: "Mathematical Mysteries: The Beauty and Magic of Numbers", Plenum Press, New York, 1996, pages 64 and 65 Volume 1: Patterns of prime distribution in "polygonal - number pyramids" You are on page Twin Prime Proof (To German translation - zur deutschen Übersetzung) 1.2. Proving the twin prime conjecture The six- wide array further helps to demonstrate the otherwise still unproven conjecture that there must be infinitely many twin primes , that is, pairs of numbers where p and p + 2 are both prime. Here is how:

44. Science News Online, Ivars Peterson's MathTrek (7/4/98): Prime Talent sum converges demonstrates the scarcity of twin primes—even though after the initialset of primes starts with 1 NJ, has verified that the conjecture is true http://www.sciencenews.org/sn_arc98/7_4_98/mathland.htm

Recently on MathTrek: First Digits 6/27/98 Prime Listening 6/20/98 Coins, Art, and Math in North Bay 6/13/98 July Prime Talent W hole numbers have all sorts of curious properties. Consider, for example, the integer 1998. It turns out that 1998 is equal to the sum of its digits plus the cubes of those digits (1 + 9 + 9 + 8 + 1 ). What's the largest number for which such a relationship holds? The answer is 1998. What about the smallest integer? That was one of the playful challenges presented by number theorist Carl Pomerance of the University of Georgia in Athens to an audience that included the eight winners of the 27th U.S.A. Mathematical Olympiad, their parents, assorted mathematicians, and others. The occasion was the U.S.A.M.O. awards ceremony on June 8 at the National Academy of Sciences in Washington, D.C. Cubes of Perfection ). What's the smallest prime the sum of whose digits is perfect? The answer is 1999. The prime 1999 also comes up in another context: 1999 = 2 . Pomerance calls any positive integer

45. Twin Primes: An Introduction To Number Theory Answer The number of twin primes is suspected to be infinite, butthat conjecture has not been proven. The cousin primes, 37 http://web.mit.edu/esp/www/Pro/HSSP2000/Classes/osm/ooze/twinPrimeNumberTheory4.

Twin Primes: An Introduction to Number Theory Requires: Prime Numbers Twin Primes Let's start by taking an unusual fact, then exploring it. Here is the fact I propose: Isn't is unusual that if you take a pair of twin primes other than 3 and 5, multiply them together, and add one, you get a number that is both A multiple of 36 and a square number 5 x 7 + 1 = 36 = 36 x 1 11 x 13 + 1 = 144 = 36 x 4 17 x 19 + 1 = 324 = 36 x 9 29 x 31 + 1 = 900 = 36 x 25 41 x 43 + 1 = 4164 = 36 x 49 59 x 61 + 1 = 3600 = 36 x 100 etc. First: Why is it always a square number? The Hint... How could you algebraically express the twin primes? How do they relate to the number in between them? How does their product relate to the number in between? The Answer... One way to look at these numbers is that the larger one (for example, 61) is n +1, the smaller (for example, 59) is n -1, and the non-prime in between (for example, 60) is n . Thus, the product of the twin primes is: n +1) x ( n n Thus, when you add one, you get n ^2, which is always a square number. Second: Why is it always a multiple of 36?

46. Number Theory remarks is to give a tight characterization of twin primes greater than three. Itis hoped that this might lead to a decision on the conjecture that infinitely http://www.math.utah.edu/~gold/numbertheory.html

Number Theory Jeffrey Frederick Gold Mathematical Interests: Twin Primes, Experimental Number Theory, Elementary Number Theory, Chinese Remainder Theorem, Covering Sets, Linear Congruences, Prime Numbers (of course), abundant numbers, odd perfect numbers, group theory, Galois theory, vectors, and more. Don H. Tucker and I have been working on the Twin Prime Conjecture for about six or seven years now. We have developed a mathematical algorithm which, when tested using a computer analogue, correctly predicted the twin primes in ascending order up to 5,000,000. Of course, the computer is never a proof (except maybe by intimidation), so we have been working on the induction argument for quite some time. It always seems to be within grasp, and just when I'm about to say, "Oh, to hell with it," I stare back down onto the page and the numbers give me something, they always give me something, something to come back and work on the problem again. Damn! I thought I'd get away!!!! A Characterization of Twin Prime Pairs, (with Don H. Tucker). Proceedings - Fifth National Conference on Undergraduate Research, Volume I, pp. 362-366, University of North Carolina Press, University of North Carolina at Asheville (UNCA), 1991. Abstract The basic idea of these remarks is to give a tight characterization of twin primes greater than three. It is hoped that this might lead to a decision on the conjecture that infinitely many twin prime pairs exist; that is, number pairs

47. Jeffrey Gold's Curriculum Vitae On a conjecture of Erdös , (with Don H. Tucker). Broken Symmetry inprimes and twin primes. (with Don H. Tucker). In preparation. http://www.math.utah.edu/~gold/vitae.html

Curriculum Vitae Up-to-date CV [PDF] [PDF] are available. Jeffrey Frederick Gold Mailing Address: 440 East Broadway Executive Suite 51 Salt Lake City, Utah 84111 Fax: (801) 933-5359 Email: gold@math.utah.edu WWW: http://www.math.utah.edu Education United States Naval Academy (Annapolis), 1987-88. University of Utah, Bachelor of Science, Physics, June 1996. University of Utah, Minor, Mathematics, June 1996. University of Cambridge (United Kingdom). Fitzwilliam College , Department of Physics, Cavendish Laboratories, Microelectronic Research Centre, 1996-97. Personal Have lived in Moline, Illinois; Castroville, California; Heidelberg, Germany Las Cruces, New Mexico ; Bangor, Maine; Honolulu, Hawaii; Annapolis, Maryland ; Cambridge, England; Albi, France; and am currently living in Salt Lake City, Utah. Fluent in German and English. Hobbies include fishing, softball, soccer, sailplane gliding, and number theory. Publications A Characterization of Twin Prime Pairs , (with Don H. Tucker). Proceedings - Fifth National Conference on Undergraduate Research, Volume I, pp. 362-366, University of North Carolina Press, University of North Carolina at Asheville (UNCA), 1991.

48. Primarily Primes Every even number can be expressed as the difference of two primes. Can youcheck this conjecture for the even numbers from 2 to 50? twin primes. http://www.dlk.com.au/beingmathematical/numbers/primarily_primes.html

Primarily Primes Prime numbers have been the source of fascination for mathematicians for centuries. Nothing has changed! It has been known for over 2000 years that there are an infinite number of primes. Euclid's proof is claimed to be one of the most beautiful proofs ever written. Euclid's Proof of the existence of an infinite number of prime numbers Every number which is not a prime (called a composite number) is itself divisible by at least one prime. To prove there are an infinite number of primes, let us assume there are not. That is, let's assume P is the largest Prime. We can then prove this is impossible. The primes are - for our sake - 2, 3, 5, 7, 11 ...... P Let us then define Q as: Q = (2 x 3 x 5 x 7 x 11 x ..... x P) + 1. If Q is divided by any of the prime numbers below it, then the remainder will be 1. So it is not divisible by any number less than it other than 1. Hence Q is prime. But Q is bigger than our largest prime P. Hence there cannot ever be a P which is the largest Prime. There are many theories which have been tested without an exception found. But that doesn't mean there is a proof. Here's some:

49. 11N: Multiplicative Number Theory Numerical data for the twinPrime conjecture. Brun's constant (sum of reciprocalsof all twin primes; Brun's constant counting twin primes. http://www.math.niu.edu/~rusin/known-math/index/11NXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11N: Multiplicative number theory Introduction History Applications and related fields Subfields Distribution of primes Primes in progressions [See also 11B25] Distribution of integers with specified multiplicative constraints Primes represented by polynomials; other multiplicative structure of polynomial values Sieves Applications of sieve methods Asymptotic results on arithmetic functions Asymptotic results on counting functions for algebraic and topological structures Rate of growth of arithmetic functions Distribution functions associated with additive and positive multiplicative functions Other results on the distribution of values or the characterization of arithmetic functions Distribution of integers in special residue classes Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx] Generalized primes and integers None of the above, but in this section Parent field: 11: Number Theory Browse all (old) classifications for this area at the AMS.

50. FOM: Twin Primes Vs. Goldbach Conjecture FOM twin primes vs. Goldbach conjecture. Peter Schuster pschust@rz.mathematik.unimuenchen.deMon, 19 Jun 2000 163004 +0200 (MET DST) http://www.cs.nyu.edu/pipermail/fom/2000-June/004160.html

FOM: twin primes vs. Goldbach conjecture Peter Schuster pschust@rz.mathematik.uni-muenchen.de Mon, 19 Jun 2000 16:30:04 +0200 (MET DST) Previous message: FOM: Re: science and constructive mathematics Next message: FOM: Some thought on "Realism" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] The problem with using Goldbach's conjecture as an example of a possibly indeterminate statement is that it is hard to imagine how it could be both false and unknowable, because a counterexample can be finitely verified. This asymmetry obscures the relationship between "unknowable" and "indeterminate" that I was trying to illustrate. Couldn't also the falsehood of "there are infinitely many twin primes" be finitely veryfied by exhibiting the greatest pair and by giving a proof that it is so? Such a proof might even be simpler than all the calculations necessary for demonstrating that some large even integer is not sum of two prime numbers. Peter Schuster. Previous message: FOM: Re: science and constructive mathematics Next message: FOM: Some thought on "Realism"

51. FOM: Re: Twin Primes Again again; Next message FOM Re twin primes again; Peter Schuster wrote I understandfrom your contributions that the twin prime conjecture is something http://www.cs.nyu.edu/pipermail/fom/2000-June/004172.html

FOM: Re: twin primes again Joe Shipman shipman@savera.com Wed, 21 Jun 2000 12:40:36 -0400 Previous message: FOM: twin primes again Next message: FOM: Re: twin primes again Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] I understand from your contributions that the twin prime conjecture is something different from Goldbach's conjecture or Fermat's last theorem. Do I correctly understand that, according to your opinion, no position is possible which simultaneously (a) does not assume that the truth-value of such "highly infinitary" statements as the twin prime conjecture is determinated from the outset; (b) does not deny the whole set of integers as a "completed whole", as something "to quantify over"; (c) does not distinguish between statements like "for each integer ..." and the corresponding "universally quantified" formula? Note that (a) is a crucial point for every constructive philosophy, if not for any pragmatic view of mathematics in general; (b) is just what I tend to assign to (Bishop's) constructive mathematics, although Bishop possibly would not agree;

52. Goldbach Conjecture Verification Computational results and graphics by Tomás Oliveira e Silva.Category Science Math Open Problems Goldbach conjecture...... In their famous memoir 2, conjecture A, Hardy and Littlewood conjectured that whenn tends to infinity R(n twin p odd prime (p1)^2 is the twin primes constant http://www.ieeta.pt/~tos/goldbach.html

Goldbach conjecture verification Introduction Results Acknowledgements References ... [Up] Introduction The Goldbach conjecture is one of the oldest unsolved problems in number theory [1, problem C1] . In its modern form, it states that every even number larger than two can be expressed as a sum of two prime numbers. Let n be an even number larger than two, and let n=p+q , with p and q prime numbers, be a Goldbach partition of n . Let r(n) be the number of Goldbach partitions of n . The number of ways of writing n as a sum of two prime numbers, when the order of the two primes is important, is thus R(n)=2r(n) when n/2 is not a prime and is R(n)=2r(n)+1 when n/2 is a prime. The Goldbach conjecture states that , or, equivalently, that , for every even n larger than two. In their famous memoir [2, conjecture A] , Hardy and Littlewood conjectured that when n tends to infinity R(n) tends asymptotically to n p-1 N2(n) = 2 C - PRODUCT - , twin (log n)^2 p odd prime p-2 divisor of n where p(p-2) C = PRODUCT - = 0.6601618158... twin p odd prime (p-1)^2

53. [math/0103191] Characterization Of The Distribution Of Twin Primes the count of primes to that point. The manner of the decrease is consistent withthe HardyLittlewood conjecture, the Prime Number Theorem, and the twin Prime http://arxiv.org/abs/math/0103191

Mathematics, abstract math.NT/0103191 Characterization of the Distribution of Twin Primes Authors: P.F. Kelly Terry Pilling Comments: 8 pages, 4 figures, Latex Subj-class: Number Theory MSC-class: 11A41 (Primary) 11Y11 (Secondary) We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like fixed probability random events. As the sequence of primes grows, the probability decreases as the reciprocal of the count of primes to that point. The manner of the decrease is consistent with the HardyLittlewood Conjecture, the Prime Number Theorem, and the Twin Prime Conjecture. Furthermore, our probabilistic model, is simply parameterized. We discuss a simple test which indicates the consistency of the model extrapolated outside of the range in which it was constructed. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Links to: arXiv math find abs

54. Maths Thesaurus: Twin Prime Conjecture Home twin prime conjecture The conjecture that there are infinitely manysets of twin primes. This has never been proved. (Find similar words). http://thesaurus.maths.org/dictionary/map/word/976

Twin prime conjecture The conjecture that there are infinitely many sets of twin primes. This has never been proved. Find similar words More general: Defined earlier: Conjecture Twin primes New search: Age: 19 Choose Language and Age Make a suggestion nrich@damtp.cam.ac.uk

55. Math 300 Lesson 4 large. twin Prime conjecture. The number of pairs of twin primes lessthan the number X is approximately 1.32X/(1+1/2+1/3+ +1/X) 2; http://www.math.odu.edu/~noren/math300/m300sp04.html

The Primes The second of four lessons in Chapter 2. Adjacent Primes Adjacent, or consecutive primes, have no primes between them. 13 and 17 are an example of adjacent primes because no prime lies between them. 17 and 23 are not adjacent primes; 19 lies between them. Large Gaps Among Primes There are gaps as large as we please between adjacent primes. recall 3!=(3)(2)(1), in general, n!=(n)(n-1)...(1) For instance, we may form 200 consecutive non-primes; 201!+2, 201!+3, 201!+4,..., 201!+201. 2 divides 201!+2 3 divides 201!+3 etc., 201 divides 201!+201 In general, for n consecutive non-primes, form (n+1)!+2, (n+1)!+3,..., (n+1)!+(n+1); 2, 3, ... , n+1, respectively, divide these numbers. Twin Primes Twin primes are consecutive odd numbers that are prime. Some examples: 3 and 5, 29 and 31, 71 and 73. Some consecutive odds that are not: 7 and 9, 31 and 33. Are there finitely many or not? Prime Number Theorem Using the notation Pn for the "nth" prime, P1=2, P2=3, P3=5, and so on, then Pn is 'approximately' (n)(1+1/2+1/3+...+1/n). More precisely, if we denote (n)(1+1/2+1/3+...+1/n) by A(n)

56. More Math News with a prize of $300 Poincaré conjecture Purported Proof Perforated (MathWorld)Two Gigantic primes with Prime A New Pair of twin primes (Science News http://math.smsu.edu/moremathnews.html

More Math News Strategies on Fourth Down, From a Mathematical Point of View (NY Times) "Math = Beauty + Truth/(Really Hard)" - an exposition of the Fields medalists' work (Salon.com) Obsessing with the Magic of Primes (NY Times) Fields Medalists and Nevanlinna Prize Winner Announced A Polynomial Time Primality Test Has Been Discovered (NY Times) The Repunit R49081 is Probably Prime Draft Proof of Catalan's Conjecture Circulated (MathWorld) 143-Year-Old Problem Still Has Mathematicians Guessing (NY Times) The EKG Sequence (Science News) 2^13,466,917 - 1 is prime! (BBC) Here is a mathematical programming contest with a prize of $300 (MathWorld) Two Gigantic Primes with Prime Digits Found (MathWorld) An archive of Putnam Competition problems (including 2001) A Hundred-dollar, Hundred-digit Challenge (requires Adobe Acrobat) A New Pair of Twin Primes (Science News) "Is Powerball a Mug's Game?" (Slate) "The Shape of the Universe: Ten Possibilities (Abstract) (American Scientist) "Bubbles and Math Olympiads" (Science News) (Science News) International Mathematical Olympiad 2001 - Problems and Results "Connoisseurs of Chaos Offer a Valuable Product: Randomness" (The New York Times) "Circle Games" (Science News) "Adding Art to the Rigor of Statistical Science" (The New York Times) "A New Solution to the Three-Body Problem" (Notices of the AMS) (Requires Adobe Acrobat Reader) The 31st Fermat Number is Composite "Why Mathematicians Now Care About Their Hat Color" (The New York Times) Largest Known Twin Primes Discovered Two Eighth-Graders Discover a Theorem in Geometry "The Story of the 120-Cell" (Notices of the AMS) (Requires Adobe Acrobat Reader)

57. Mathematics For Elementary Teachers - "Math Activity 3.3" Find the numbers of twin primes in intervals of 100 (1 to 100, 100 to 200, etc.).Form a conjecture about the occurrence of twin primes for such intervals. http://www.rscs.net/~gb2570/Math_Investigations/MA_4.1.html

COMPUTER INVESTIGATION 4.1 The computer program FREQUENCY OF PRIMES on the Mathematics Investigator prints and counts the numbers and types of primes in given intervals. Starting Points for Investigations 1. How many prime numbers are less than 100? Check other intervals of 100 (100 to 200, 200 to 300, etc.) to determine the numbers of primes. Form a conjecture about the numbers of primes in these intervals. 2. Pairs of numbers such as 3 and 5, 5 and 7, 11 and 13, whose difference is 2 are called twin primes. It is not known whether or not there are an infinite number of such primes. Find the numbers of twin primes in intervals of 100 (1 to 100, 100 to 200, etc.). Form a conjecture about the occurrence of twin primes for such intervals. 3. In #2 you found consecutive primes whose difference is 2. There are also consecutive primes whose difference is 4, such 7 and 3, 17 and 13, 23 and 19. Check intervals of 100 to see if such primes exist in each interval. Do the number of such primes appear to be increasing or decreasing from interval to interval? 4. Are there consecutive primes whose difference is any even number? For example, consecutive primes whose difference is 6? 8? 10? Are there consecutive primes whose difference is any odd number (1, 3, 5, etc.)? Investigate these questions and form a conjecture based on your evidence. (You may be interested to know that there are conjectures in mathematics involving even numbered differences of primes which as yet are unproved.)

58. Tim Melrose : Problems With Primes whether there are infinitely many of these twin primes. However most mathematiciansbelieve the answer is ‘yes’. A more famous conjecture regarding primes http://www.maths.adelaide.edu.au/pure/pscott/history/tim/tmp6.html

Problems with Primes Other Facts About Primes Unproved Conjectures References U nproved Conjectures Primes have a tendency to arrange themselves in pairs of the form ( p p +2): for example 3 and 5, 5 and 7, 17 and 19. This is also evident among much larger numbers such as 29,879 and 29,881. Such primes are called twin primes or prime pairs, A more famous conjecture regarding primes is the Goldbach Conjecture , named after Christian Goldbach (1) Every even number greater than or equal to 4 is the sum of two primes; for example (It is easy to verify that this conjecture fails for odd numbers, 11 or example.) In the letter Goldbach also expressed the following belief: (2) Every integer n greater than or equal to 5 is the sum of three primes. As far as is known, Euler did not prove (1), but neither Euler nor anyone else has been able to find a counter-example. This conjecture has since been tested for all even numbers up to at least 10 and found to be true. This still remains one of the great unsolved conjectures of mathematics. Pierre de Fermat conjectured that is prime for any non-negative integer n . The conjecture was proven to be incorrect by Euler in 1732 who showed that F More recently analysis of these so-called Fermat numbers have found no other primes above F . However no-one has yet proved that F is the largest Fermat prime.

59. Pictures Of Primes, II This is in good agreement with a conjecture of Hardy and Littlewood, which givesthe density of twin primes as 1.32/log(x)^2. The expected number of twin http://www.mathematik.uni-muenchen.de/~forster/primes2.html

Pictures of Primes II In the above 128 x 128 matrix the n-th square is black iff the number 10^50 + 2n + 1 is prime. By the prime number theorem, the density of primes in this range is approximatively 1/log(10^50) = 1/115, so we would expect about 2^15/115 = 285 primes in this picture. The actual number is 269. The first prime after 10^50 is 10^50 + 151. There are three twin primes (10^50 + x_i, 10^50 + x_i + 2) in this picture, with x_i = 18307, 19891, 29749. This is in good agreement with a conjecture of Hardy and Littlewood, which gives the density of twin primes as 1.32/log(x)^2. The expected number of twin primes in our interval of length 2^15 = 32768 according to this conjecture is 3.26.. . data file data file data file data file ... Otto Forster (forster@rz.mathematik.uni-muenchen.de), 95-05-29/97-04-30

60. Mathematics Until these conjecture were tied to FLT, FLT had been regarded by most Largest knowntwin primes The largest known twin primes are 1706595 * 2 ^ 11235 + 1 http://sciboard.louisville.edu/math.html

Mathematics Click on a question to know the answer Q. What is the current status of Fermat's last theorem? Q. Has the Four Colour Theorem been solved? Q. What are the largest prime numbers? Q. I have this complicated symbolic problem (most likely a symbolic integral or a DE system) that I can't solve. What should I do? ... Return to Question and Answers Q. What is the current status of Fermat's last theorem? (There are no positive integers x , y , z and n > 2 such that x ^ n + y ^ n = z ^ n) Ans. The status of FLT has remained remarkably constant. Every few years, someone claims to have a proof ... but oh, wait, not quite. Meanwhile, it is proved true for ever greater values of the exponent (but not all of them), and ties are shown between it and other conjectures (if only we could prove one of them), so it has been for quite some time. It has been proved that for each exponent, there are at most a finite number of counter-examples to FLT. Here is a brief survey of the status of FLT. It is not intended to be 'deep',but rather is intended for non-specialists.

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