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Topic: Composite number

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Mersenne prime

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Highly composite number

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	PlanetMath: highly composite number
		The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360.
		"highly composite number" is owned by Kevin OBryant.
		This is version 4 of highly composite number, born on 2003-06-11, modified 2006-12-08.
	www.planetmath.org /encyclopedia/HighlyCompositeNumber.html (84 words)

	PlanetMath: composite number
		A composite number is a positive integer which is not prime and not equal to 1.
		2 is not composite, as it is prime.
		This is version 6 of composite number, born on 2002-05-23, modified 2004-09-10.
	planetmath.org /encyclopedia/Composite.html (120 words)

	PlanetMath: highly composite number
		The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360.
		Alaoglu and P. Erdös, On highly composite and similar numbers.
		This is version 4 of highly composite number, born on 2003-06-11, modified 2006-12-08.
	planetmath.org /encyclopedia/HighlyCompositeNumber.html (84 words)

	Prime and Composite Numbers
		The numbers 0 and 1 are neither prime nor composite.
		Therefore all numbers that end with five and are greater than five are composite numbers.
		The prime numbers between 2 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
	www.aaamath.com /B/fra63ax2.htm (115 words)

	Composite Number -- from Wolfram MathWorld
		The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16,...
		Note that the number 1 is a special case which is considered to be neither composite nor
		There are an infinite number of composite numbers.
	mathworld.wolfram.com /CompositeNumber.html (156 words)

	Divisibility
		One whole number is divisible by another if, after dividing, the remainder is zero.
		A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
		A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
	www.mathgoodies.com /lessons/vol3/divisibility.html (1549 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: )
		A "composite" number is a number like 18 which can be written as smaller numbers multiplied together, like 63 or 29.
		A "prime" number is a number like 17 which cannot be written as smaller numbers multiplied together without using "1" as one of only two numbers.
		A "prime factor" of a number is a factor of the number which also happens to be a prime number.
	www.bonus.com /contour/askdrmath/http@@/mathforum.org/library/drmath/view/57050.html (492 words)

	Highly composite number (Site not responding. Last check: )
		Roughly speaking, the necessary conditions for a number to be a highly composite number are that it has prime factors that are as small as possible, but not too many of the same: e.g.
		Because the number of divisors of a number is obtained by adding 1 to the exponents of its prime factorisation and multiplying them together, the exponents of the prime factorisation of a highly composite number can not increase.
		Many of these numbers are used in traditional systems of measurement, and tend to be used in engineering designs, due to their ease of use in calculations involving fractions.
	www.abacci.com /wikipedia/topic.aspx?cur_title=Highly_composite_number (447 words)

	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7306 words)

	Composite number (Site not responding. Last check: )
		A composite number is a positive integer with three or more divisors.
		Because the number 1 and the composite number itself are not prime numbers, a composite number can also be defined as "a non-prime number with one or more prime factors".
		The smallest composite number is the number 4
	www.casimiro.com /wiki/en/wikipedia/c/co/composite_number.html (162 words)

	Number Definitions
		Irrational numbers are numbers that can't be expressed as a quotient of two integers, such as pi or square roots; they can only be expressed as infinite, non-repeating decimals.
		A square number is obtained by multiplying a number by itself (e.g., 1, 4, 9, 25,...).
		A triangular number is a number obtained as the sum of consecutive integers.
	www.learner.org /channel/courses/learningmath/number/keyterms.html (2526 words)

	Highly composite number (Site not responding. Last check: )
		Because the number of divisors of a number is obtained by adding 1 to the exponents of its prime factorisation and multiplyingthem together, the exponents of the prime factorisation of a highly composite number can not increase.
		Highly composite numbers higher than 6 are also abundant numbers.One need only look at the three or four highest divisors of a particular highly composite number to ascertain this fact.
		Many of these numbers are used in traditional systems of measurement, and tend to be used in engineering designs, due totheir ease of use in calculations involving fractions.
	www.therfcc.org /highly-composite-number-103058.html (333 words)

	Gregory West
		The idea of a prime number, a number that is greater than one and is divisible only by itself and one, has fascinated mathematicians because of its role as the building blocks of other numbers.
		For example, the numbers two, three, five, and seven are prime, while six is not, since it is divisible by either two or three (and would instead be called a composite number).
		Composites that pass the test of Fermat’s Little Theorem are uncommon, but the fact that Fermat’s theorem did not inspire algorithms that achieved both speed and reliability meant that, to mathematicians, the algorithms were fundamentally flawed.
	www.its.caltech.edu /~sciwrite/journal03/west.html (3312 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: )
		The numbers zero and one are considered to be neither prime nor composite.
		A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not be distinct, hence squares of primes are included).
		A composite number with three distinct prime factors is a sphenic number.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=composite_number (314 words)

	The Mathematical Tourist
		The study of prime numbers is one of the few areas still left in mathematics in which the concepts, questions and experiments are still simple enough to intrigue both amateur and professional mathematicians.
		The number 333333331 is a composite with factors 17 and 19607843.
		The number 32, for instance, is the sum of 13 and 19.
	www.fortunecity.com /emachines/e11/86/tourist2b.html (2578 words)

	Brainboost - what is a whole number of a composite number
		Prime And Composite Numbers Prime And Composite Numbers - (5TH GRADE STANDARDS OF LEARNING) - STANDARDS - Objective - The student will determine if a whole number is a prime number or a composite number.
		Background For Teachers: - Students learned to classify whole numbers from 2 to 20 as composite or prime, and 0 and 1 as neither prime nor composite, in fifth grade.
		A prime number is a whole number that only has two factors which are itself and one.
	www.brainboost.com /search.asp?Q=what+is+a+whole+number+of+a+composite+number&lfmq=1 (249 words)

	Composite number for pi satisfies Euler's equation.
		is an irrational number that cannot be expressed as the root of an algebraic equation having rational coefficients, it is called a transcendental number.
		is a transcendental number, i.e., an irrational number that is not, and cannot be, the root of an algebraic equation having rational coefficients.
		Transcendental number — An irrational number that cannot be expressed as the root of an algebraic equation having rational coefficients.
	members.aceweb.com /r-logan/fullbook.html (4935 words)

	Number Theory Lesson
		Defining numbers as prime or composite was first documented in history as early as 300 B.C. mathematician by the name of Euclid documented his definitions in his book of elements.
		Because we are looking at the sets of all positive integers, prime numbers, and composite numbers, we are dealing with infinite sets.
		Yes this works on determining if a number is a multiple of 9 to determine composite or prime, but it can be used for a broader scale.
	tiger.towson.edu /~jbobb1/eezine/primesvscomposites.htm (1942 words)

	MathSteps: Grade 5: Prime Factors: What Is It?
		Counting numbers which have more than two factors (such as six, whose factors are 1, 2, 3 and 6), are said to be composite numbers.
		When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.
		Since a number is divisible by two if it ends in either 0, 2, 4, 6, or 8, it should be noted that two is the only even prime number.
	www.eduplace.com /math/mathsteps/5/b (449 words)

	Prime number - ExampleProblems.com
		A natural number that is greater than one and is not a prime is called a composite number.
		Prime numbers are of fundamental importance in number theory.
		The prime number theorem says that the proportion of primes less than x is asymptotic to 1/ln x (in other words, as x gets very large, the likelihood that a number less than x is prime is inversely proportional to the number of digits in x).
	www.exampleproblems.com /wiki/index.php/Prime_number (3311 words)

	Prime and Composite Numbers - Math Lesson Plan, Thematic Unit, Activity, Worksheet, or Teaching Idea
		Now tell them, when a number such as 4, 6, and 8 has more than two factors, it is called a composite number.
		Now tell them, when a number such as 3, 5 and 7 has only two factors (1 and itself), it is called a prime number.
		1 is neither a prime nor a composite.
	www.lessonplanspage.com /MathPrimeAndCompositeNumberTiles67.htm (573 words)

	Prime or Composite Numbers
		A number may be made by multiplying two or more other numbers together.
		The numbers that are multiplied together are called factors of the final number.
		All numbers have a factor of one since one multiplied by any number equals that number.
	www.aaamath.com /g8-72-prime-or-composite.html (161 words)

	The Prime Glossary: composite number
		One reason is that many secret codes (e.g., RSA) and much of the security of the Internet (e.g., PGP) depends in part on the relative difficulty of factoring large numbers.
		The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
		It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length...
	primes.utm.edu /glossary/page.php?sort=Composite (254 words)

	Highly Composite Numbers (Site not responding. Last check: )
		Highly composite numbers have sparked a number of interesting observations, some of which I will elaborate on here.
		Together, these two prime numbers "contribute" xy factors of H. Now, let's further suppose that the contribution of these two primes is a constant, a, and that xy=a.
		In round numbers, for a given number of factors of H, H is minimized when the ratio of one plus the exponents of 2 and 3 is close to ln(3):ln(2), or about 1.585.
	mcraeclan.com /mathhelp/BasicNumberFactorsHighlyComposite.htm (1545 words)

	Composite number - Definition, explanation
		A composite number is a positive integer that can be factored as a product of two or more prime numbers.
		The number one is considered to be neither prime nor composite.
		The integer 14 is a composite number because it can be factored as 2 × 7.
	www.calsky.com /lexikon/en/txt/c/co/composite_number.php (234 words)

	Prime Numbers — FactMonster.com
		Any number greater than 5 that ends in a 5 can be divided by 5.
		Except for 0 and 1, a number is either a prime number or a composite number.
		A composite number is defined as any number, greater than 1, that is not prime.
	www.factmonster.com /ipka/A0876084.html (225 words)

	The On-Line Encyclopedia of Integer Sequences
		The number of composite numbers <= n (A065855) = n - pi(n) (A000720) - 1.
		The composite numbers have the semiprimes A001358 as primitive elements.
		A. Bojarincev, Asymptotic expressions for the n-th composite number, Univ. Mat.
	www.research.att.com /cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002808 (258 words)

	How to determine whether a number is prime or composite Math Lesson Plan, Thematic Unit, Activity, Worksheet, or ...
		A prime number is an integer greater than 1 which has no factors besides 1 and itself.
		divisible by 11, it is NOT prime and therefore composite.
		There is a set of 13 consecutive composite numbers in the integers 1-200.
	www.lessonplanspage.com /MathPrimeVsCompositeNumbers7HS.htm (400 words)

	Factoring: (Site not responding. Last check: )
		If a number n>1 is not prime then it is called a composite number.
		This is a process where we break a composite number down into a product of prime numbers.
		The key is that you start with a long division problem consisting of the number you want to factor in the dividend, and a prime number as the divisor.
	home.earthlink.net /~ubingc/math/mth209/factoringnum.htm (597 words)

	Learning Math: Composite Numbers and Prime Numbers
		A whole number greater than 1 that has only two factors (1 and itself) is called a prime number.
		A whole number greater than 1 that has more than two factors is called a composite number.
		Except 1, any number which is not a prime number is a composite number.
	www.syvum.com /cgi/online/serve.cgi/squizzes/math/prime.tdf (289 words)

	prime composite numbers
		A composite number is a whole number that has more than two factors.
		Note that the numbers 0 and 1 are neither prime nor composite.
		The prime factorization of a whole number is the number written as the productof its prime factors.
	www.algebra-online.com /prime-composite-numbers-1.htm (541 words)

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