41. Affine Arithmetic Project Affine arithmetic A CorrelationSensitive Variant of Interval arithmetic. Affinearithmetic (AA) is a self-validated model for numerical computation. http://www.dcc.unicamp.br/~stolfi/EXPORT/projects/affine-arith/Welcome.html

Affine Arithmetic: A Correlation-Sensitive Variant of Interval Arithmetic Researchers: Jorge Stolfi Luiz Henrique de Figueiredo Ronald van Iwaarden Marcus Vinicius Alvim Andrade ... João Luiz Dihl Comba Project description Affine arithmetic (AA) is a self-validated model for numerical computation. Like standard interval arithmetic (IA), it can provide guaranteed bounds for the computed results, taking into account input, truncation, and rounding errors. Unlike interval arithmetic, it keeps track of correlations between computed and input quantities, and is therefore resistant to the catastrophic loss of precision often observed in long interval computations. In affine arithmetic, a quantity x is represented as a first-degree ("affine") polynomial x0 + x1 e1 + x2 e2 + ··· + xk ek where x0, x1,... xk are known real numbers, and e1, e2,... ek are dummy variables, whose value is only known to be in [-1 .. +1]. Each dummy variable ei represents some source of uncertainty or error in the quantity x - which may come from input data uncertainty, formula truncation, arithmetic rounding, etc. A dummy variable that appears in two variables x, y

42. K-THEORY AND ARITHMETIC (30 September - 4 October 2002) Isaac Newton Institute, Cambridge, UK; 30 September 4 October 2002.Category Science Math Number Theory Events Past Events......Isaac Newton Institute for Mathematical Sciences, Cambridge,UK. KTHEORY AND arithmetic 30 September - 4 October 2002. http://www.newton.cam.ac.uk/programs/NST/nstw03.html

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK K-THEORY AND ARITHMETIC 30 September - 4 October 2002 Programme Participants Organisers: S Lichtenbaum ( Brown ), VP Snaith ( Southampton Theme: This workshop will concentrate on the aspects of the interplay between algebraic K-theory, arithmetic and algebraic geometry. Particular emphasis will be placed upon applications of the recently developed homotopy theory of geometric and motivic categories. In addition to lectures on current results, a number of expository lectures will be scheduled to provide researchers and graduate students in related areas with an opportunity to learn about these new techniques. Topics of current interest in this area include: Beilinson-Soulé conjectures, Bloch-Kato conjecture, Beilinson-Borel regulators, Kato-Parshin-Saito higher class field theory, Lichtenbaum-Quillen conjecture, Milnor K-theory, motivic cohomology, Brumer-Coates-Sinnott conjectures, polylogarithms and special values of L-functions. Participants will include: M Ando (UIUC), S Bloch (Chicago), D Burns (KCL), G Carlsson (Stanford), R de Jeu (Durham), WG Dwyer (Notre Dame), H Esnault (Essen), I Fesenko (Nottingham), P Goerss (Northwestern), JPC Greenlees (Sheffield), M Hanamura (Kyushu), L Hesselholt (MIT), M Hovey (Wesleyan), P Hu (Chicago), A Huber (Leipzig), U Jannsen (Regensburg), JF Jardine (UWO), B Kahn (Paris VII), I Kriz (Michigan), M Levine (Northeastern), S Lichtenbaum (Brown), I Madsen (Aarhus), M Mahowald (Northwestern), F Morel (Paris VII), DC Ravenel (Rochester), J Rognes (Oslo), M Rost (Ohio State), P Schneider (Muenster), AJ Scholl (Cambridge), S Schwede (Bielefeld), V Snaith (Southampton), C Soulé (IHES), NP Strickland (Sheffield), B Totaro (Cambridge), V Voevodsky (IAS), C Weibel (Rutgers), N Yagita (Ibaraki)

43. Arithmetic Geometry Isaac Newton Institute, Cambridge; January to July 1998.Category Science Math Number Theory Events Past Events......Isaac Newton Institute for Mathematical Sciences. arithmetic GeometryJanuary to July 1998. Organisers JL ColliotTh eacutel egravene http://www.newton.cam.ac.uk/programs/AMG/

Programme outline Workshops Junior Membership Participants: Long stay Short Stay Mailing list Contacts ... Programme Report Isaac Newton Institute for Mathematical Sciences Arithmetic Geometry January to July 1998 Organisers: Programme theme The origin of this subject was the study of solutions of Diophantine Equations - that is the the search for integer or rational solutions of systems of polynomial equations - using geometric methods. Today, Arithmetic Geometry has expanded to cover a wide range of topics central to Number Theory, Algebraic Geometry and other branches of pure mathematics. The programme will highlight several areas of this vast subject, including: arithmetic of algebraic cycles, motivic cohomology, rational points on algebraic varieties, Arakelov theory, and regulators and special values of L -functions. As a part of the European Commission's Training and Mobility of Researchers programme, a three-month post-doctoral position is offered for research work related to the programme. See http://www.univ-rennes1.fr/labos/IRMAR/arithgeom.html

44. Skill In Arithmetic Netscape 6 will be all right. This is a complete course in arithmetic. Mental arithmetic.How do we add mentally by composing a 10? How do we add by endings? http://www.themathpage.com/ARITH/arithmetic.htm

S k i l l i n A r i t h m e t i c Home This is a complete course in arithmetic. While the student (and teacher) will find the usual written methods, we emphasize that rather than something we're meant to do formally on paper, arithmetic is something we do naturally in our heads. Introduction Prologue 1 Elementary Addition The commutative law of addition. Sums less than 10. Composing 10 itself. Sums between 10 and 20. Prologue 2 The Multiplication Table Lesson 1 Powers of 10 Which numbers are the powers of 10 ? How do we read a whole number? What do we mean by the place value of a digit? How do we write a whole number in expanded form How do we multiply a whole number by a power of 10? Lesson 2 The Meaning of Decimals Which numbers are the decimal units ? What is the function of the decimal point? How do we read a decimal? How do we compare decimals? Lesson 3 Multiply by Powers of 10, Divide by Powers of 10 The Meaning of Percent How do we multiply a decimal by a power of 10? How do we divide a decimal by a power of 10?

45. Primary Arithmetic, Or Math Four booklets, and more, that you can easily copy. One of math games for ages 4-8., two about teaching Category Science Math Education......Four free booklets on basic primary math or arithmetic (one of games), andmore,for K3 teachers,Spec.Ed.teachers,and homeschooling parents. http://www3.telus.net/public/m.games/welcome.html

Gordon's Games, Simple Math, Not So Simple Math, and Not Just Math A RETIREMENT PROJECT The above four booklets, and more, on this website are intended to be a resource for those who teach Primary Math, K-3, ages 4 to 8 Beginning teachers, home schooling parents, spec. ed. teachers, teachers of teachers, and teachers wishing to supplement a text could find ideas of value here. C H O I C E S CONTENTS : a short description of the four booklets and links to them. BOOKLETS : how to copy from this site, plus links. TERMS : if you wish to buy the booklets, postage paid. No profit is being made. This is intended to be a service to those who can't make copies, or don't wish to. NEW : more games and activities; using playing cards with the games. NEW! Make a simple bookmark or email address page your browser can read. -for all who gather up a lot of these -allows you to sort and name as you wish, get what you want quickly, easily save a backup copy to disk, and use your addresses with other browsers. MORE MATH SITES : links to other sites. WEB CENTER : will take you to most of the many places on this site and speed up return visits for those copying material.

46. Flix Productions Animated Educational Software Flix Productions, award winning educational software, Animated arithmeticsoftware. Animated arithmetic. The Animated arithmetic http://www.flixprod.com/arithmetic.html

Animated Arithmetic The "Animated Arithmetic CD" for Windows and Win 95 teaches addition, subtraction, multiplication and division for children from 1st through 4th grades. It provides exercises in addition and subtraction with and without regrouping. Problems can involve up to 9 digits. More than just a drill program, progressive help is given as needed to instruct the child to solve the problems. The multiplication and division problems are based on the multiplication table from 1 to 10, it teaches "mental math" in a painless way. Progressive help is given as needed when the student is having difficulty with a particular problem (not just a Wrong! response from the computer). Once ten problems are completed, the student gets to visit the game room. There are over 20 puzzles using 3D animation and sound on the registered CD ROM. The child can choose 12, 24, or 48 pieces. Hints for solving the puzzles are available, or the child can have the computer solve the puzzle and enjoy the (mostly silly) animation. There is also a maze game where the child can play mazes of varying complexity (which are rewarded with an animation when solved), or make and save their own mazes for their friends to try and solve. You can even choose to have the computer solve the maze - watching it find it's way out can be fascinating. There is over 160 Meg of animation and sound in the games on the CD!

47. Binary Arithmetic Connected An Internet Encyclopedia Binary arithmetic Up Connected An InternetEncyclopedia Next Bridging. Binary arithmetic. For some important http://www.freesoft.org/CIE/Topics/19.htm

Connected: An Internet Encyclopedia Binary Arithmetic Up: Connected: An Internet Encyclopedia Up: Topics Up: Concepts Prev: Acronyms Next: Bridging Binary Arithmetic For some important aspects of Internet engineering, most notably IP Addressing , an understanding of binary arithmetic is critical. Many strange-looking decimal numbers can only be understood by converting them (at least mentally) to binary. All digital computers represent data as a collection of bits . A bit is the smallest possible unit of information. It can be in one of two states - off or on, or 1. The meaning of the bit, which can represent almost anything, is unimportant at this point. The thing to remember is that all computer data - a text file on disk, a program in memory, a packet on a network - is ultimately a collection of bits. If one bit has two different states, how many states do two bits have? The answer is four. Likewise, three bits have eight states. For example, if a computer display had eight colors available, and you wished to select one of these to draw a diagram in, three bits would be sufficient to represent this information. Each of the eight colors would be assigned to one of the three-bit combinations. Then, you could pick one of the colors by picking the right three-bit combination. A common and convenient grouping of bits is the byte or octet , composed of eight bits. If two bits have four combinations, and three bits have eight combinations, how many combinations do eight bits have? If you don't want to write out all the possible byte patterns, just multiply eight twos together - one two for each bit. Two times two is four, so the number of combinations of two bits is four. Two times two times two is eight, so the number of combinations of three bits is eight. Do this eight times - or just compute two to the eighth power - and you discover that a byte has 256 possible states.

48. Arithmetic Problems And Kids Math Help Practice Exercises Level I Games and activities to help kids learn skills such as addition, subtraction, multiplication, division, Category Kids and Teens School Time Math arithmetic......Activities in Math for Kids and arithmetic Practice Exercises. Learn Addition IV.arithmetic Problems Math Exercises for Kids Level I. Min http://www.syvum.com/math/arithmetic/level1.html

Syvum Home K-12 SAT GRE ... Advertise here Math SyvumBook to Help Kids : Level I Buy this SyvumBook for offline use. Recommended Age: 6-7 years. Knowledge Required of 1-2 digit numbers. Go To : Kids Math Help Level II Kids Math Help Level III Kids Math Help Level IV : Level I Min/Max Number : Math help for Kids to Find Smallest and Greatest Numbers Place Value : Math help for Kids to Understand Units and Tens Places ... Contact Info

49. Arithmetic : Decimal Arithmetic , Fractions , Exercises & Problems arithmetic Exercises Problems. All exercises below are interactiveand feature dynamic content. arithmetic Exercises Problems Index http://www.syvum.com/squizzes/arithmetic/

Syvum Home K-12 SAT GRE ... Quiz Games > Arithmetic Try our other QUIZ GAMES MATH Quiz Games WORD PROBLEMS ... IQ TESTS All exercises below are interactive and feature dynamic content. After clicking "Score and Show Answer(s)", click the "Try another set" button at the bottom to get a new set of questions. Enjoy contributions from Syvum members here. Do you WISH TO CONTRIBUTE too ? Exercises Recommended for Arithmetic Exercises : Decimal Addition > 11 years / Grade 5 Arithmetic Learn addition of decimals with 1 or 2 decimal places. Arithmetic Exercises : Decimal Subtraction > 11 years / Grade 5 Arithmetic Learn subtraction of decimals with 1 or 2 decimal places. Arithmetic Exercises : Decimal Multiplication > 11 years / Grade 5 Arithmetic Learn multiplication of decimals with 1 or 2 decimal places by an integer. Arithmetic Exercises : Decimal Division > 11 years / Grade 5 Arithmetic Learn division of decimals with 1 or 2 decimal places by an integer. Arithmetic Exercises : Simplification of Fractions > 11 years / Grade 5 Arithmetic Learn to reduce fractions to their lowest terms.

50. The Devil’s Arithmetic The Devil’s arithmetic. Door to the Holocaust. News Special. Introduction. Hannahdidn't want to go to Passover Seder; she didn't want to remember anymore. http://www.fsu.edu/~CandI/ENGLISH/webquests/devil.htm

Door to the Holocaust News Special Introduction Hannah didn't want to go to Passover Seder; she didn't want to remember anymore. But when she symbolically opens the door to welcome the prophet Elijah, she is suddenly transported back in time to 1940s Poland. Once the Nazis send Hannah to a concentration camp, she realizes how important it is to remember the past. Your mission, if you choose to accept it, is a big one! You are three news journalists who are doing an in depth TV news special about the Holocaust for the Passover holiday. You have been told about a magic door in the local synagogue that opens on Passover but, the thing is, it transports you back in time to the Holocaust. You must be brave to relive this horrific event in history but people must remember the past, and understand what the Jewish people went through! The Task As part of the news team, you will accept one of the following roles: The Journalist (News Anchor)- Your job is to interview the camp members, and learn their stories. The Photographer- Your job is to collect pictures of the camp, and the people there.

51. Variable Precision Arithmetic Lawry Schonfelder's variable precision package, using many of the new features introduced in Fortran 90.Category Computers Programming Source Code Increasing Precision......Variable Precision arithmetic. Version 1.1 A Fortran 95 Module. By JL.Schonfelder.Contents. 2.5 arithmetic operations. 2.5.1 Basic arithmetic operations. http://www.pcweb.liv.ac.uk/jls/vpa11.htm

Variable Precision Arithmetic Version 1.1 A Fortran 95 Module By J.L.Schonfelder Contents 1. Introduction 2. Specification 2.1 The Module 2.2 The Type ... SIGN . Introduction This module, written in standard conforming Fortran 95, provides a set of facilities for the support of floating-point arithmetic that is of variable and in principle arbitrary precision. It can also handle very large ranges of numbers. It has been produced to enable applications that require very high and possibly varying numeric precision to be implemented easily. It exploits the semantic-extension data-abstraction capabilities of the Fortran 95 language to define a suitable number data-type and the fundamental arithmetic operations to manipulate numbers of this type. Thus application programs can largely work with such numbers as if they were normal REAL values. while every care has been taken to ensure the released module is error free, it has been subject to careful testing by the author, no guarantee is given or implied that the released module is without fault or is fit for any specific purpose. The author accepts no liability for any damages howsoever caused resulting from any use of this package. . Specification The Module The module is named and the facilities of the module can be accessed by the inclusion of the statement USE VARIABLE_PRECISION_ARITHMETIC The Type The type is The interpretation of the type depends on the values of a small number of integer parameters. In the distributed version these are set as appropriate for an IEEE arithmetic system where the default integer is 32 bit, with a range of 9, and

52. Arithmetic arithmetic the mathematics of integers, rational numbers, real numbers, or complexnumbers under addition, subtraction, multiplication, and division. http://math.about.com/cs/arithmetic/

zfp=-1 About Homework Help Mathematics Arithmetic Search in this topic on About on the Web in Products Web Hosting Mathematics with Deb Russell Your Guide to one of hundreds of sites Home Articles Forums ... Help zmhp('style="color:#fff"') Subjects ESSENTIALS Grade By Grade Goals Math Formulas Multiplication Fact Tricks ... All articles on this topic Stay up-to-date! Subscribe to our newsletter. Advertising Free Credit Report Free Psychics Advertisement Arithmetic Guide picks Basic arithmetic addressing the four operations with integers, rational and real numbers and including measurement, geometry and base ten. Order of Operations - Tutorial Although computations are often correct, the answer is often wrong! Why? Too many students forget the order of operations. The order of operations is critical in solving mathematical problems. Add, Subtract, Multiply, Divide A variety of lessons, tutorials, worksheets and printables to assist with the four operations in mathematics/arithmetic. Base Ten and Place Value Concepts Tutorials and lessons for understanding place value systems. An early and solid understanding of base ten can lead to mathematical success in later years. Multiplication Tables and Help Multiplication tables, strategies and help for those needing additional work to commit the multiplication facts to memory.

53. Arithmetic Calculator When in doubt, punch it out! Other Calculators. Recommend This Calculator!Lessons, Forums, Homework, Puzzles, Newsletter, Advertise, Search. http://www.mathgoodies.com/calculators/calculator.htm

When in doubt, punch it out! Other Calculators Recommend This Calculator! Lessons Forums ... Home Join The Math Goodies Newsletter! Name: Email Address: Delivery Format: TEXT Manage Subscriptions

54. Clock Arithmetic You need to have a Java enabled browser to view this Java applet.If your browser supports Java, but you are seeing this mesasge http://www.shodor.org/interactivate/activities/clock1/

You need to have a Java enabled browser to view this Java applet. If your browser supports Java, but you are seeing this mesasge, you probably need to enable Java Please help us by suggesting enhancements or reporting bugs in this program. Or, send us other questions or comments about this activity. The Shodor Education Foundation, Inc.

55. Floating-point Arithmetic Under the Hood. Floatingpoint arithmetic. In the JVM, floating-pointarithmetic is performed on 32-bit floats and 64-bit doubles. http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.html

Advertisement: Support JavaWorld, click here! October 1996 HOME FEATURED TUTORIALS COLUMNS FORUM ... JAVA TIPS INDEX JavaWorld Services Free JavaWorld newsletters ProductFinder Education Resources White Paper Library NEW! Rational Resources Under the Hood Floating-point arithmetic A look at the floating-point support of the Java virtual machine Summary All Java programs are compiled into class files which contain bytecodes, the machine language of the Java virtual machine. This article takes a look at the bytecodes that implement the floating-point capabilities of Java. (2,500 words) By Bill Venners Printer-friendly version Mail this to a friend Page 1 of 2 Advertisement elcome to another installment of Under The Hood . This column aims to give Java developers a glimpse of the hidden beauty beneath their running Java programs. This month's column continues the discussion, begun last month , of the bytecode instruction set of the Java virtual machine (JVM). This article takes a look at floating-point arithmetic in the JVM, and covers the bytecodes that perform floating-point arithmetic operations. Subsequent articles will discuss other members of the bytecode family. The main floating points The JVM's floating-point support adheres to the IEEE-754 1985 floating-point standard. This standard defines the format of 32-bit and 64-bit floating-point numbers and defines the operations upon those numbers. In the JVM, floating-point arithmetic is performed on 32-bit floats and 64-bit doubles. For each bytecode that performs arithmetic on floats, there is a corresponding bytecode that performs the same operation on doubles.

56. Logic And Integer Arithmetic This article takes a look at the bytecodes that implement the logical and integerarithmetic capabilities of Java. (4000 words). Logic and integer arithmetic. http://www.javaworld.com/javaworld/jw-11-1996/jw-11-hood.html

Advertisement: Support JavaWorld, click here! November 1996 HOME FEATURED TUTORIALS COLUMNS FORUM ... JAVA TIPS INDEX JavaWorld Services Free JavaWorld newsletters ProductFinder Education Resources White Paper Library NEW! Rational Resources Under the Hood Logic and integer arithmetic A look at the bytecodes of the Java virtual machine that perform logical and arithmetic operations Summary All Java programs are compiled into class files that contain bytecodes, the machine language of the Java virtual machine. This article takes a look at the bytecodes that implement the logical and integer arithmetic capabilities of Java. (4,000 words) By Bill Venners Printer-friendly version Mail this to a friend Page 1 of 3 Advertisement elcome to yet another installment of Under The Hood . This column aims to give Java developers a glimpse of the mysterious mechanisms clicking and whirring beneath their running Java programs. This month's article continues the discussion of the bytecode instruction set of the Java virtual machine (JVM). The article takes a look at integer arithmetic and logic in the JVM, and covers the bytecodes that perform logical and arithmetic operations on integers. Subsequent articles will discuss other members of the bytecode family. Integer arithmetic The Java virtual machine offers bytecodes that perform integer arithmetic operations on ints and longs. Values of type byte, short, and char are converted to int before they take part in arithmetic operations. For each bytecode that performs arithmetic on ints, there is a corresponding bytecode that performs the same operation on longs.

57. Things Of Interest To Number Theorists Papers and surveys by Ed Schaefer.Category Science Math Elliptic Curves and Modular Forms...... http://math.scu.edu/~eschaefe/nt.html

Here is a list of my papers followed by postscript files of eight lectures. 2-descent on the Jacobians of hyperelliptic curves, Journal of Number Theory, (51), 1995, 219-232. Class groups and Selmer groups, Journal of Number Theory, (56), 1996, 79-114. This paper gives bounds on the index of the intersection of a Selmer group and a quotient of the dual of part of a class group in each of the two groups. Arithmetic and geometry of the curve 1+y^3 = x^4 (with M.J. Klassen), Acta Arithmetica, (74), 1996, 241-257. This paper shows that the set of Weierstrass points (the flexes) is the same as the set of rational points over the field Q(zeta_12) and is a torsion packet. It also finds the bitangents to this curve and bases for the 2- and 3-torsion of the Jacobian. A simplified Data Encryption Standard algorithm, Cryptologia, (20), 1996, 77-84. This paper gives a method of explaining the DES algorithm to a cryptography class. Computing a Selmer group of a Jacobian using functions on the curve, Mathematische Annalen, (310), 1998, 447-471. This paper gives a general algorithm for finding Selmer groups for the Jacobians of curves. It includes discussions of the assumptions such algorithms seem to be based on. The Selmer group is for an isogeny, over a number field, from an abelian variety to the Jacobian of a curve where the kernel of the isogeny is killed by a power of a prime. Explicit descent for Jacobians of cyclic covers of the projective line (with B. Poonen), Journal fuer die Reine und Angewandte Mathematik, (488), 1997, 141-188. This paper gives an algorithm for finding the 1-zeta_p Selmer group for the Jacobian of a curve y^p = f(x).

58. Active The arithmetic of Active Management. William F. Sharpe. This proves assertion number1. Note that only simple principles of arithmetic were used in the process. http://www.stanford.edu/~wfsharpe/art/active/active.htm

The Arithmetic of Active Management William F. Sharpe Reprinted with permission from The Financial Analysts' Journal Vol. 47, No. 1, January/February 1991. pp. 7-9 Association for Investment Management and Research Charlottesville, VA "Today's fad is index funds that track the Standard and Poor's 500. True, the average soundly beat most stock funds over the past decade. But is this an eternal truth or a transitory one?" "In small stocks, especially, you're probably better off with an active manager than buying the market." "The case for passive management rests only on complex and unrealistic theories of equilibrium in capital markets." Statements such as these are made with alarming frequency by investment professionals . In some cases, subtle and sophisticated reasoning may be involved. More often (alas), the conclusions can only be justified by assuming that the laws of arithmetic have been suspended for the convenience of those who choose to pursue careers as active managers. If "active" and "passive" management styles are defined in sensible ways, it

59. ALOHA Mental Arithmetic ALOHA Mental arithmetic provide a fast mental maths learning and enable fastcalculation without and calculation devices. What is Mental arithmetic? http://www.alohama.com/index.shtml

window.defaultStatus="ALOHA Mental Arithmetic" Mental Arithmetic ALOHA Middle-East ALOHA Abacus Museum (348 type of abacuses) Year One students learn mental maths in school now ... Australia Franchise The Management Message from the MD ALOHA Guest book Sign Guest Book View Guest Book Nurture a New and Better Generation... Highlight Australia Centre Update Chinese Version What is Mental Arithmetic? Mental arithmetic is a form of training which will enhanced a child ability to do calculation without the aid of any instruments such as the calculator, abacus and etc. The child will be able to calculate with speed and accuracy using his own mental power. Home Company Profiles ALOHA Gallery Program ... ALOHA Mental Arithmetic Last updated

60. Large Primes In Arithmetic Progression Join the search for an example of 6 titanic primes in arithmetic progression.Category Science Math Number Theory Prime Numbers......Large Primes in arithmetic Progression. This page is a repository forlarge primes in arithmetic progression (AP). Under Construction! http://ksc9.th.com/warut/ap/

Large Primes in Arithmetic Progression This page is a repository for large primes in arithmetic progression (AP). Under Construction! If you want to join the search for an example of 6 titanic primes in AP, contact Paul Jobling at Paul.Jobling@WhiteCross.com Length 3 475977645*2^44639+1 (13447 digits, 475977645*2^44640-1 (13447 digits, common difference = 475977645*2^44639-2 1593*2^27757+1 (8359 digits, common difference = 1593*2^27757-2 87114*10^1100+1 (1105 digits) 174228*10^1100-1 (1106 digits) common difference = 87114*10^1100-2 Harvey Dubner 10312266581350704550*(2^3423-2^1141)-6*2^1141-7 (1050 digits) 10312266581350704550*(2^3423-2^1141)-6*2^1141-1 (1050 digits) 10312266581350704550*(2^3423-2^1141)-6*2^1141+5 (1050 digits) common difference = 6 (3 consecutive primes in AP, Tony Forbes more 10^1000+13186668131*10^495+1 (1001 digits, palindrome) 10^1000+14266666241*10^495+1 (1001 digits, palindrome) 10^1000+15346664351*10^495+1 (1001 digits, palindrome) common difference = 1079998110*10^495 Length 4 112968765*2^6000+1 (1815 digits) 133479045*2^6000+1 (1815 digits) 153989325*2^6000+1 (1815 digits) 174499605*2^6000+1 (1815 digits) common difference = 20510280*2^6000 172079565*2^5000+1 (1514 digits) 237055875*2^5000+1 (1514 digits) 302032185*2^5000+1 (1514 digits) 367008495*2^5000+1 (1514 digits) common difference = 64976310*2^5000 67819605*2^4000+1 (1212 digits) 84731955*2^4000+1 (1213 digits) 101644305*2^4000+1 (1213 digits) 118556655*2^4000+1 (1213 digits) common difference = 16912350*2^4000

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