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Topic: Table of prime factors

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Table of divisors

405 (number)

700 (number)

Fermat prime

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Prime factorization algorithm

Divisibility rule

18 (number)

Prime number

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Factorization

23 (number)

Decimal

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	Prime factor - Wikipedia, the free encyclopedia
		In number theory, the prime factors of a positive integer are the prime numbers that divide into that integer exactly, without leaving a remainder.
		The prime factorization of a positive integer is a list of the integer's prime factors, together with the maximum power of each prime factor that divides the integer exactly.
		For a positive integer n, the number of prime factors of n and the sum of the prime factors of n (not counting multiplicity) are examples of arithmetic functions of n that are additive but not completely additive.
	en.wikipedia.org /wiki/Prime_factor (220 words)

	Table of prime factors - Wikipedia, the free encyclopedia
		This table contains the integer factorization for the numbers from 1 to 1002.
		The number 1 has only one divisor, namely 1, is not a prime and does not have any prime factors.
		The sum osfgf the prime factors of 1 is 0.
	en.wikipedia.org /wiki/Table_of_prime_factors (83 words)

	Divisor - Wikipedia, the free encyclopedia
		In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder.
		A divisor of n that is not 1, −1, n or −n is known as a non-trivial divisor; numbers with non-trivial divisors are known as composite numbers, while prime numbers have no non-trivial divisors.
		Factoring Calculator -- Factoring calculator that displays the prime factors and the prime and non-prime divisors of a given number.
	en.wikipedia.org /wiki/Divisor (925 words)

	[No title]
		According to the great mathematician Gauss [1], 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.
		Table 1 (located at the end of this paper) displays composite numbers, their factorization, the number of non-witnesses, denoted nw(n), and the upper bound of non-witnesses.
		Table 3 shows a list of numbers r (where 2r+1 and 4r+1 are prime), the sample size, the number of non-witnesses, and the proportion of non-witnesses to the sample size.
	www.ma.iup.edu /MAA/proceedings/vol1/higgins.doc (2301 words)

	Prime factor (Site not responding. Last check: 2007-10-08)
		The prime factors of a positive integer are the prime numbers that divide into that integer exactly, without leaving aremainder.
		The prime factorization of a positive integer is alist of the integer's prime factors, together with the maximum power of each prime factor that divides the integer exactly.
		For a positive integer n, the number of prime factors of n and the sum of the primefactors of n (not counting multiplicity) are examples of arithmetic functions of n that are additive but not completely additive.
	www.therfcc.org /prime-factor-133874.html (181 words)

	NationMaster.com - Encyclopedia: Table of divisors (Site not responding. Last check: 2007-10-08)
		The tables below list all of the divisors of the numbers 1 to 1000.
		A divisor of an integer n is an integer m, say, for which n/m is again an integer (which is necessarily also a divisor of n).
		I have no plans at the moment to do similar edits on the Table of prime factors, but I think it really needs it.
	www.nationmaster.com /encyclopedia/Table-of-divisors (400 words)

	Serebella Contents Table of prime factors---Table of standard electrode potentials for half-re (Site not responding. Last check: 2007-10-08)
		Table of prime factors---Table of standard electrode potentials for half-re
		A collection of arithmetic calculations arranged in a table, such as multiplications in a multiplication table.
		The greatest factor in the decision was the need for public transportation.
	www.serebella.com /encyclopedia/contains-418797-418800-Table_of_prime_factors-Table_of_standard_electrode_potentials_for_half-re.html (1562 words)

	The Largest Known Primes
		For example, the prime divisors of 10 are 2 and 5; and the first six primes are 2, 3, 5, 7, 11 and 13.
		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.
		Because the way the largest numbers N are proven prime is based on the factorizations of either N+1 or N-1, and for Mersennes the factorization of N+1 is as trivial as possible (a power of two).
	primes.utm.edu /largest.html (1152 words)

	Prime Territory
		Primes appear to be the building blocks of multiplication—you can express all positive integers as a unique set of primes factors—but there is not a simple equation to generate a list of primes, nor is there a simple way to determine if any given number is prime.
		Not only are primes good for play, it turns out that prime numbers are extremely important in the area of cryptography.
		I begin the article with a brief note on factoring, people interested in the meat of the argument might skip to the binary strings or prime patterns articles.
	www.descmath.com /prime (878 words)

	Puzzle 196. Consecutive integers with the same quantity of prime factors
		The last is necessary since the table for K=1 indicates that a solution is not allowed to be extendable to the previous or next number.
		I first computed sets of probable primes around 338 digits and then tried different combinations of these for a, b and c until the cofactors (x+1)/14 and (x+2)/15 were both probable primes.
		Proving the probable primes would take decades with Primo unless a method to search for solutions with easily provable prime factors can be found.
	www.primepuzzles.net /puzzles/puzz_196.htm (1024 words)

	Divisibility
		In the last lesson, we learned to find all factors of a whole number to determine if it is prime or composite.
		Thus, if we could find one factor of 621, other than 1 and itself, we could prove that 621 is composite.
		Since 18 is divisible by 9, 9 is a factor of 18.
	www.mathgoodies.com /lessons/vol3/divisibility.html (1562 words)

	Factors of googolplex plus power of ten
		Please let me know if you found another prime factor of the numbers shown below or if you found a use for this table by filling the form.
		See also the related table that includes known prime factors of the first 1000 numbers starting from googolplex.
		See 57441 known prime factors (mostly found using the program written by David Broadhurst and enhanced by Phil Carmody).
	www.alpertron.com.ar /GOOGOL2.HTM (90 words)

	Table of prime factors: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-08)
		This table contains the integer factorization[For more info, click on this link] for the numbers from 1 to 1002.
		In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime...
		The sum of the prime factors of 1 is 0.
	www.absoluteastronomy.com /encyclopedia/t/ta/table_of_prime_factors.htm (3472 words)

	BMCC Math Tutorials -- Numbers -- Greatest Common Factor (Site not responding. Last check: 2007-10-08)
		Recall from the section on factors that a factor is any whole number that divides a product evenly (with no remainder).
		The common factors for 30 and 48 are 2, 3, and 6.
		Now we want to make a table showing the prime factorization for the numbers, in exactly the same manner we did for determining the least common multiple using prime factorization.
	www.bmcc.org /nish/MathTutorials/Numbers/n-gcf.htm (1073 words)

	Math Forum - Ask Dr. Math Archives: Finding Prime Factors
		Factoring is an idea you might be familiar with from multiplication.
		However, 12 is not a prime number, because 1 * 12 = 12, 2 * 6 = 12, and 3 * 4 = 12.
		Prime factorization means finding all the prime numbers that are factors of a number.
	mathforum.org /library/drmath/sets/select/dm_prime_factors.html (462 words)

	Prime factor (Site not responding. Last check: 2007-10-08)
		The prime factors of a positive integer are the prime numbers that divide into that integer exactly leaving a remainder.
		The prime factorization of a positive integer is a of the integer's prime factors together with maximum power of each prime factor that the integer exactly.
		The prime factors of 6 are and 2.
	www.freeglossary.com /Prime_factor (306 words)

	Number and Operations Session 5, Part C:Factors
		Some numbers factor into two factors only, while others may have two factors, one or both of which can be factored further.
		An important distinction can be made between the terms "factor" and "prime factor." By factors, we mean all the factors of a number.
		The numbers on the bottom branch of this tree are the prime factors of 12 -- they can't be factored any further.
	www.learner.org /channel/courses/learningmath/number/session5/part_c/no_flash.html (491 words)

	Prime factors #1
		If we find one in the first half of the table, successively add that number to the position and set the resulting entry to zero for the rest of the table.
		By the time we get halfway through the table, only primes are left which we can then pack by removing all the 0's from the table.
		Take the highest prime in the table, add 2 (it's an odd number and we know there won't be anymore even primes), then for table entries less than or equal to the square root of this number, try dividing by the number and check for a remainder.
	www.delphiforfun.org /Programs/PrimeFactors1.htm (918 words)

	[No title]
		A prime factors is a factor that is a prime number.Discussion on Prime Numbers and Prime Factors.
		Develop a game to show 'is a factor', 'is not a factor'.Composite and prime numbers.Identifying and comparing composite and prime numbers.Identify prime and composite numbers between 0 and 100.Differentiating between composite and prime numbers.Prime numbers are numbers that have only two factors.
		A factor is a whole number that can divide another number leaving a remainder zero, e.g.
	www.sdnp.org.gy /ncerd/resources/maths/number/number6.doc (1675 words)

	Random Prime Factorization
		A function telling you if a given number is prime, and then a sort of loop dividing the original number until it reduces to the unity.
		but there are "factorizers" (programs to factorize or prime factor numbers) with the original or my personal favorite being the one that made the name.
		instead of checking the list of prime factors for repeats, you can just test when you find that n/i is whole, you can then take n/(i*m) with m equaling the n/i to start and decreasing by 1 each iteration.
	www.physicsforums.com /showthread.php?t=31750&page=1 (2487 words)

	Talk:Table of prime factors - InformationBlast
		I agree with Patrick and I propose that we omit the 1s since we know that 1 is a divisor/factor of every integer.
		I prefer the first one, but I do not own wikipedia :-) On the other side at the Table of divisors we should leave 1s as they are, since a 'common' multiplicative arithmetic function τ(n) == d(n) == NumDiv(n) returns them for all n.
		I know there were some problems with the tables for some well-known planets and stars.
	www.informationblast.com /Talk:Table_of_prime_factors.html (228 words)

	Answer to Example
		The set S consists of all numbers that are the sum of three consecutive prime numbers.
		A prime number is an integer greater than 1 that has only two positive factors: 1 and itself.
		Using this table, one can obtain a list of all the prime numbers within a specificied range.
	www.gomath.com /members/test/tutorial/section2/p1.html (259 words)

	Tim Lynch's Review of "Prime Factors"
		While "Prime Factors" had a few weaknesses associated with it, primarily in the stage-setting and the "pleasure planet" concept, it's one of the first episodes "Voyager" has had that has truly allowed these characters to be _human_ (in a broad sense), with all the assorted foibles and bad judgment calls inherent therein.
		"Prime Factors"'s main weakness, alas, was the lead-up to the main crisis of the show, that being the conflict over getting the "spatial trajector" technology.
		While the concept of a planet devoted purely to pleasure is neither a new nor a bad one in the slightest, I wish it didn't seem so incredibly stilted in the execution this week.
	www.dcs.gla.ac.uk /~hwloidl/TL/voy1/prime.html (1486 words)

	Table of prime factors: Encyclopedia topic (Site not responding. Last check: 2007-10-08)
		The updated page can be found at: table of prime factors
		This table contains the integer factorization (integer factorization: more facts about this subject) for the numbers from 1 to 1002.
		The number 1 (1: The smallest whole number or a numeral representing this number) has only one divisor, namely 1, is not a prime and does not have any prime factors.
	www.absoluteastronomy.com /reference/table_of_prime_factors (2569 words)

	How many primes are there?
		The most widely distributed was D. Lehmer's table of primes to 10,006,721 [Lehmer14].
		The Prime Number Theorem: The number of primes not exceeding x is asymptotic to x/log x.
		Gauss was also studying prime tables and came up with a different estimate (perhaps first considered in 1791), communicated in a letter to Encke in 1849 and first published in 1863.
	primes.utm.edu /howmany.shtml (1731 words)

	The cutting edge of metaphysical research.
		The analysis of primes is by position only, which is to say according to what adds up to each of them.
		Then interpret the current number according to this factoring and to what adds up to it as shown in its position in the table.
		Observe that the table proceeds from the most most general, the simplest factors in simplest combination, to the particular, the higher and more complicated.
	www.visibleandinvisible.com /ifss (801 words)

	Table of prime factors (Site not responding. Last check: 2007-10-08)
		This table contains the integer factorization for the numbers 1-1002.
		Pull this table out for extra guests on your patio or an improvisational session with your laptop.
		Multivalued function, American Physical Society, Tyagaraja, Thyagaraja, Table of prime factors, Annamacharya, Lord Venkateswara, TTD, Tirumala Tirupati Devasthanams, Linnik's theorem, Tirumala, Balaji, Hyatt Hotel disaster, Numbat, Parallel computation, Pagan, Myanmar, Dom Tower, Anoratha, A.
	www.freeglossary.com /Table_of_factors (177 words)

	Untitled
		This paper introduces the reader to the Rabin-Miller probabilistic primality test, the concept of non-witnesses to compositeness, and the problem of determining the number of non-witnesses to compositeness.
		The problem of determining if a given number is prime is of great interest to both computer scientists and mathematicians.
		Note: This table was produced after analyzing a great amount of data similar to that shown in Table 2.
	www.ma.iup.edu /MAA/proceedings/vol1/higgins.htm (2868 words)

	Sum of Prime Factors of Quadratics (Site not responding. Last check: 2007-10-08)
		This polynomial is famous because it gives primes for many values of x, related to the fact that the discriminant is -163, which is the largest with class number = 1.
		Given any two of the prime factors of a solution pqr, we can substitute into this equation to get a quadratic in the third factor, from which we can infer two possible values of the third factor.
		If the other root of the quadratic happens to be a prime, then it gives another solution of equation (1).
	www.mathpages.com /home/kmath006/part6/part6.htm (1259 words)

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