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Topic: Unique prime

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	Sum of Unique Prime Factors Sequence
		a(2) is a(1) + the sum of the unique prime factors a(1), or 1+(1)=2.
		a(3) is a(2) + the sum of the unique prime factors a(2), or 2+(2)=4.
		a(5) is a(4) + the sum of the unique prime factors a(4), or 6+(2+3)=11.
	home.mindspring.com /~kikiriki/id11.html (99 words)

	Prime factor - Wikipedia, the free encyclopedia
		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.
		The prime factors of 6 are 3 and 2.
	en.wikipedia.org /wiki/Prime_factor (201 words)

	Unique prime - Wikipedia, the free encyclopedia
		A prime p ≠ 2, 5 is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1 / p, is equivalent to the period length of the reciprocal of q, 1 / q.
		At present, more than fifty unique primes or probable primes are known.
		Though they are rare, based on the occurrence of repunit primes and probable primes, it is conjectured strongly that there are infinitely many unique primes.
	en.wikipedia.org /wiki/Unique_prime (242 words)

	Encyclopedia: Prime number (Site not responding. Last check: 2007-11-07)
		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).
		A probable prime is an integer which, by virtue of having passed a certain test, is considered to be probably prime.
		With this definition, the primes of the field Q of rational numbers are represented by the standard absolute value function (known as the "infinite prime") as well as by the p-adic valuations on Q, for every prime number p.
	www.nationmaster.com /encyclopedia/Prime-number (7323 words)

	Integer factorization - Wikipedia, the free encyclopedia
		It is known to be in BQP because of Shor's algorithm.
		Interestingly, the decision problem "is N a composite number?" (or equivalently: "is N a prime number?") appears to be much easier than the problem of actually finding the factors of N.
		Manindra Agarwal, Nitin Saxena, Neeraj Kayal, "PRIMES is in P", Preprint, August 6, 2002, http://www.cse.iitk.ac.in/news/primality.html
	en.wikipedia.org /wiki/Integer_factorization (892 words)

	The Prime Glossary: unique prime
		The reciprocal of every prime p (other than two and five) has a period, that is the decimal expansion of 1/p repeats in blocks of some set length (see the period of a decimal expansion).
		Samuel Yates defined a unique prime (or unique period prime) to be a prime which has a period that it shares with no other prime.
		Caldwell, "Unique (period) primes and the factorization of cyclotomic polynomial minus one," Mathematica Japonica, 46:1 (1997) 189--195.
	primes.utm.edu /glossary/page.php?sort=UniquePrime (238 words)

	NSSH Part 622 (00-Exhibit 1) \| NRCS Soils
		Prime farmland is not excessively eroded or saturated with water for long periods of time, and it either does not flood frequently during the growing season or is protected from flooding.
		Prime farmland information may be supplemented with separate designations of soil map units that have state-wide, local, or unique importance as farmland capable of producing these crops.
		Prime farmland is land that has the best combination of physical and chemical characteristics for producing food, feed, forage, fiber, and oilseed crops, and is also available for these uses (the land could be cropland, pastureland, rangeland, forest land, or other land, but not urban built-up land or water).
	soils.usda.gov /technical/handbook/contents/part622.html (5446 words)

	Unique prime -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, a unique prime is a certain kind of (An integer that has no integral factors but itself and 1) prime number.
		Unique primes were first described by (Click link for more info and facts about Samuel Yates) Samuel Yates in 1980.
		It can be shown that a prime p is of unique period n (Click link for more info and facts about iff) iff there exists a (The number 1 and any other number obtained by adding 1 to it repeatedly) natural number c such that
	www.absoluteastronomy.com /encyclopedia/u/un/unique_prime.htm (203 words)

	Farmland Protection Program \| New Mexico NRCS (Site not responding. Last check: 2007-11-07)
		Prime - Prime farmland is land that has the best combination of physical and chemical characteristics for producing food, feed, fiber, forage, oilseed, and other agricultural crops with minimum inputs of fuel, fertilizer, pesticides, and labor, and without intolerable soil erosion, as determined by the Secretary of Agriculture.
		Prime farmland includes land that possesses the above characteristics but is being used currently to produce livestock and timber.
		Unique farmland - Unique Farmland is land other than prime farmland that is used for production of specific high-value food and fiber crops, as determined by the Secretary.
	www.nm.nrcs.usda.gov /Programs/frpp/nm-frpp-soils-cult-res-criteria.html (359 words)

	L4.html
		A prime number is is positive integer that has exactly two positive integer divisors.
		Note: this theorem is really 2 theorems, the first is that n can be factored into primes in some way, and the second is that the factorization is unique, up to the order of the primes.
		We say p in S is a prime if we cannot write p=a*b where a and b are in S and they are not units of S. Note the units of S are just 1 and -1.
	www.math.sfu.ca /~gfee/Math342/L41.html (1533 words)

	prime -- Encyclopædia Britannica (Site not responding. Last check: 2007-11-07)
		On the basis of his knowledge that numbers of this form are prime for values of n from 1 through 4, the French mathematician Pierre de Fermat (1601–65) conjectured that all numbers of this form are prime.
		The prime minister serves under the chief of state (even if the chief of state has only titular or ceremonial powers), except in those rare cases in which the chief of state assumes the functions of prime minister.
		Includes a list of the largest known primes, definitions of the various types, and details on the processes for determining whether or not a number is a prime.
	www.britannica.com /eb/article-9061382?tocId=9061382 (905 words)

	Prime Factors and Run-Length Compression
		Although the primes in the factorization can be arranged in any order, the collection primes and their quantity in the factorization is unique.
		Because all integers have a unique prime factorizations (ignoring order of the primes), we can always express any positive integer as a unique sequence, S(n), of powers of each of the primes in order.
		Therefore, using the sequence of primes, we have been able to develop a one-to-one mapping between the positive integers and the set of all sequences of non-negative integers which converge to zero.
	www.students.uwosh.edu /~piehld88/primeseq.htm (820 words)

	Integer factorization (Site not responding. Last check: 2007-11-07)
		In mathematics, the integer prime-factorization (also known as prime decomposition) problem is this: given a positive integer, write it as a product of prime numbers.
		The factorization is always unique, according to the fundamental theorem of arithmetic.
		The easiness of prime testing is a crucial part of the RSA algorithm, as it is necessary to find large prime numbers to start with.
	www.sciencedaily.com /encyclopedia/integer_factorization (866 words)

	Broco Inc. - World Leader in Welding Products
		It consists of the Prime Cut torch, 20 feet of 3/8" oxygen hose and power cable, striker plate assembly with 20 feet of power cable, leather shield for piercing operations, 2 battery clamps, welding gloves and 2 collets for adapting either 1/4" or 3/8" rods to the torch.
		Prime Cut rods are available in 3/16", 1/4", 3/8" and 1/2" diameters and varying lengths.
		Prime Cut torch assembly with 20' of 3/8" oxygen hose and 20' of power cable, striker plate with 20' cable, battery clamps, leather shield, welding gloves, safety goggles, collets to fit all Prime Cut rod sizes, and a plastic tool box-type case.
	www.brocoinc.com /primecut.html (1432 words)

	Prime and Unique Agricultural Lands and the National Environmental Policy Act (NEPA)
		The accompanying memorandum on Analysis of Impacts on Prime or Unique Agricultural Lands in Implementing the National Environmental Policy Act was developed in cooperation with the Department of Agriculture.
		In general, prime farmlands have an adequate and dependable water supply from precipitation or irrigation, a favorable temperature and growing season, acceptable acidity or alkalinity, acceptable salt and sodium content, and few or no rocks.
		Examples of soils that qualify as prime farmland are Palouse silt loam, 0 to 7 percent slopes; Brookston silty clay loam, drained; and Tama silty clay loam, 0 to 5 percent slopes.
	ceq.eh.doe.gov /nepa/regs/exec81180.html (1040 words)

	Quantum-like Chaos in Prime Number Distribution and in Turbulent Fluid Flows
		The model concepts are applicable to the emergence of unique prime number spectrum from the underlying substratum of continuum real number field.
		In number theory, prime numbers are unique numbers and the prime number theorem(PNT) states that z/lnz gives approximately the number of primes less than or equal to z [Rose, 1995].
		The important result of the study is that the prime number spectrum is the same as the eddy energy spectrum for quantum-like chaos in atmospheric flows and the spectra follow the universal inverse power law form of the statistical normal distribution.
	www.geocities.com /CapeCanaveral/Lab/5833/prime3/Prime3.html (5122 words)

	Prime and Important Farmland \| North Carolina NRCS
		Criteria used for prime and unique farmlands were published January 31, 1978 in the Federal Register and amended in June 17, 1994.
		The soils are drained and the drainage system is adequate to maintain the water table at a sufficient depth during the growing season to allow cultivated crops common to the area to be grown.
		In general, soils that have a special set of properties that are unique for producing certain high-value crops meet the requirements for unique farmland.
	www.nc.nrcs.usda.gov /programs/soilsurvey/primefarmland.html (536 words)

	Unique prime - Definition up Erdmond.Com (Site not responding. Last check: 2007-11-07)
		A prime ''p'' ≠ 2, 5 is called unique iff there is no other prime ''q'' such that the period_length of its reciprocal, 1 / ''p'', is equivalent to the period length of the reciprocal of ''q'', 1 / ''q''.
		Unique primes were first described by Samuel_Yates in 1980.
		Preservation of prime and unique agricultural lands in the perspective of national goals and policies (Staff paper)
	www.erdmond.com /Unique_prime.html (141 words)

	Prime Factor Configuration Pattern Numbers
		The reasoning behind this lies in the fact that with 12, the squared prime (2) is smaller than the prime that is not squared (3), whereas with 18, the prime that is squared (3) is larger than the prime that is not squared (2).
		Another way of creating numbers out of prime factor configuration patterns would be to treat the two classes (as represented by 12 and 18) the same.
		Unlike the case with simple banding using primes, the visual result of using pfcpns is but subtly different from the visual result of using any of the other systems of disguising and squeezing numbers.
	www.washingtonart.net /whealton/PFCN.html (1259 words)

	Prime Factorization Software Reviews: Find prime factors and closest primes; Find prime factors and closest primes
		A program to find prime numbers and pairs of primes, to decompose numbers into their prime constituents, to find all factors of any positive integer up to 2,147,483,645, and to plot Erdos-Kac and Palmen Color histograms.
		This attractive, handy little prime number calculator takes any number up to twenty digits, and then factorizes all the unique prime numbers that evenly divide into the number that was entered into the field.
		CFB Primes is an optimised PalmOS program which can find the prime factors and closest primes of any integer number up to one billion (US) in a few seconds or less.
	www.softcetera.com /all/prime-factorization.htm (465 words)

	Lectures 4 & 5: Prime Numbers & Unique Factorization, Math 413 (Number Theory)
		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.
		An analysis of primes in the ring of Gaussian Integers is in an appendix to this chapter.
		Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
	www.math.umbc.edu /~campbell/Math413Spr05/Notes/4-5_Primes_UniqueFactor.html (988 words)

	A comprehensive introduction to prime numbers
		A prime number p is a positive integer (not 1) that is only divisible by 1 and p.
		A major use of Mersenne numbers is in the search for the largest (un)known prime, for almost all of the largest known primes in history have been Mersenne primes.
		This new prime is the 35th known Mersenne prime and is 420,921 digits long.
	www.geocities.com /CapeCanaveral/Lab/3550/prime.htm (1496 words)

	Mn/DOT - OTS, PPG HPDP, Farmland Impacts
		Agricultural land includes prime farmlands, unique farmlands, and farmlands other than prime or unique that are of statewide or local importance.
		Prime farmland is land that has the best combination of physical and chemical characteristics for producing food, feed, fiber, forage, oilseed, and other agricultural crops with minimum inputs of fuel, fertilizer, pesticides, and labor, and without intolerable soil erosion, as determined by the Secretary of Agriculture.
		Unique farmland is land other than prime farmland that is used for production of specific high-value food and fiber crops, as determined by the Secretary of Agriculture.
	www.dot.state.mn.us /tecsup/xyz/plu/hpdp/book2sg/farm.html (1106 words)

	NumberTheory - PineWiki
		The remaining numbers 0 and 1 are by convention neither prime nor composite; this allows us to avoid writing "except 0 or 1" in a lot of places later.
		If n is prime, there is nothing to prove; this provides a base case of n=2 and n=3 as well as covering larger values of n that are prime.
		is the exponent in the prime factorization of n on the i-th largest of all primes (e.g.
	pine.cs.yale.edu /pinewiki/NumberTheory (1891 words)

	Number and Operations Session 5, Part C:Factors
		A prime number is a number with exactly two factors.
		For example, the number 1 is not a prime number because it only has one factor, 1.
		The number 3 is a prime number because it has exactly two factors, 1 and 3.
	www.learner.org /channel/courses/learningmath/number/session5/part_c (487 words)

	Chapter 3.4 South and East Beltways
		Several of these prime farmland soils are mapped as occurring withing the project area.
		Because scores for all alternatives are all less than 160, no further consideration is required and the project is considered to have a minor effect on prime and unique farmland soils.
		The no build alternative has no adverse impact on farmland or prime and unique farmland soils in the project area, other than that necessary for construction of the proposed future roadway network improvements.
	www.fhwa.dot.gov /nediv/ch3-4.htm (580 words)

	FIC : Farming on the Edge: Methodology (Site not responding. Last check: 2007-11-07)
		State by state, the areas in red represent concentrations of prime and/or unique farmland coinciding with that state's most rapidly developing area(s).
		It is also important to keep in mind that we focused solely on threats to prime and unique farmland.
		We then determined acreage amounts of prime and unique farmland within each of the 33,000 mapping units included in the map database.
	www.farmlandinfo.org /farmland_technical_resources/index.cfm?function=article_view&articleID=29268 (613 words)

	A factorization and prime number program - Factorizer
		A program to find all factors of any positive integer less than 2^31 - 2, to decompose numbers into their prime constituents, to find prime numbers and pairs of primes, and to plot Erdos-Kac and Palmen Color histograms.
		Factorizer is a Windows program to find factors of numbers up to 2,147,483,646 and to find primes, pairs of primes and Palmen colors of numbers.
		In addition a "filter" condition may be set to allow examination of numbers with a constant offset from an arithmetical or a geometrical progression, e.g., just those numbers of the form 7*n - 12 or 10n + 2.
	www.acidfiles.com /Education/Mathematics/Factorizer.html (286 words)

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