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Topic: Sieve of Eratosthenes

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	PlanetMath: sieve of Eratosthenes
		The sieve of Eratosthenes is the number-theoretic version of the principle of inclusion-exclusion.
		In the typical application of the sieve of Eratosthenes one is concerned with estimating the number of elements of a set
		This is version 7 of sieve of Eratosthenes, born on 2004-01-24, modified 2006-09-05.
	planetmath.org /encyclopedia/SieveOfEratosthenes2.html (232 words)

	PlanetMath: sieve of Eratosthenes
		The sieve of Eratosthenes is a simple algorithm for generating a list of the prime numbers between
		For many years, the sieve of Eratosthenes was the fastest known algorithm for listing primes.
		This is version 3 of sieve of Eratosthenes, born on 2002-05-22, modified 2004-11-22.
	planetmath.org /encyclopedia/SieveOfEratosthenes.html (113 words)

	Biographies of Eratosthenes
		Eratosthenes is known for being a mathematician and the librarian of Alexandria.
		Eratosthenes studied at the museum, where he became successful and became the director of the museum with his wide knowledge of literature, mathematics and astronomy.
		Eratosthenes based his measurement of the earth on the assumptions that the earth is round and the sun's rays are parallel.
	users.rcn.com /mwhitney.massed/eratos_bios.html (1604 words)

	Sieve of Eratosthenes - Uncyclopedia
		Sieve of Eratosthenes is a mathematical tool not disimilar to a colander, used to determine whether a number is prime or not.
		Sieve of Eratosthenes is whilst is is useful for catching prime numbers, it also traps other primes like Optimus Prime and prime real estate.
		Sieve of Eratosthenes is not particularly accurate, it has difficult in removing surds, unreal numbers and imaginary numbers.
	uncyclopedia.org /wiki/Sieve_of_Eratosthenes (240 words)

	Eratosthenes
		Eratosthenes was born in Cyrene, Greece, which is now known as Libya, in South Africa, in 276 B.C.E..
		This sieve, which is called, the Sieve of Eratosthenes, is still important today in number research theory.
		Eratosthenes observed that the sun shone directly down a well at high noon on the day of the summer solstice in Syene and that it cast a shadow in Alexandria, directly south of where the well was.
	www.math.wichita.edu /history/men/eratosthenes.html (578 words)

	Sieve of Eratosthenes - Wikipedia, the free encyclopedia
		In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer.
		It is the predecessor to the modern Sieve of Atkin, which is faster but more complex.
		Wheel factorization is often applied on the list of integers to be checked for primality, before Sieve of Eratosthenes is used, to increase the speed.
	en.wikipedia.org /wiki/Sieve_of_Eratosthenes (390 words)

	eratosthenes sieve
		Eratosthenes was the third librarian of the famous Alexandrian library, which was placed in a temple of the Muses called the Mouseion.
		The sieve is meant to keep only prime numbers - sometimes they are called the building blocks of all numbers - and to let all other numbers 'go through'.
		You can use the Sieve of Eratosthenes to find any other pairs of twin primes - try by working on a bigger sieve to see how many twin primes are there between 2 and 200.
	www.mathsisgoodforyou.com /artefacts/sieve.htm (389 words)

	Eratosthenes
		Eratosthenes was one of the most learned men of antiquity, and wrote on a great number of subjects.
		Eratosthenes' greatest achievement was his measurement of the earth.
		Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
	www.nndb.com /people/712/000095427 (511 words)

	Eratosthenes
		Eratosthenes died at an advanced age from voluntary starvation, induced by despair at his blindness.
		Eratosthenes also conceived the "Sieve of Eratosthenes ", a method of identifying prime numbers.
		Sieve is the class that calls all others.
	www.math.utah.edu /~alfeld/Eratosthenes.html (1967 words)

	eratosthenes sieve
		Eratosthenes was the third librarian of the famous Alexandrian library, which was placed in a temple of the Muses called the Mouseion.
		The sieve is meant to keep only prime numbers - sometimes they are called the building blocks of all numbers - and to let all other numbers 'go through'.
		You can use the Sieve of Eratosthenes to find any other pairs of twin primes - try by working on a bigger sieve to see how many twin primes are there between 2 and 200.
	mathsisgoodforyou.com /artefacts/sieve.htm (389 words)

	Sieve of Eratosthenes from Interactive Mathematics Miscellany and Puzzles
		Eratosthenes (276-194 B.C.) was the third librarian of the famous library in Alexandria and an outstanding scholar all around.
		He is remembered by his measurement of the circumference of the Earth, estimates of the distances to the sun and the moon, and, in mathematics, for the invention of an algorithm for collecting prime numbers.
		The Sieve of Eratosthenes appears also in disguise of a sequential process on a triangular grid.
	www.cut-the-knot.org /Curriculum/Arithmetic/Eratosthenes.shtml (346 words)

	Cantor Arts Center - Archived Press Release
		The Sieve of Eratosthenes, which is made of steel and is 23 feet tall, is sited on the north side of the Cantor Arts Center near the conjunction of Lomita Drive and Campus Drive.
		Fabricated in 1999, The Sieve of Eratosthenes is typical of di Suvero's sculptures in providing multiple readings and viewpoints as the spectator walks around it.
		According to the donors Daniel Shapiro and Agnes Gund, the dedication of The Sieve of Eratosthenes in honor of Emeritus Professor John Merryman is especially appropriate.
	www.stanford.edu /dept/suma/news_room/archived_acquisitions_sieve.html (639 words)

	Sieve of Eratosthenes
		The Sieve of Eratosthenes is a method of factoring all of the numbers in a given range.
		As far as I am concerned the terms 'Sieve of Eratosthenes' and sieve are interchangeable it we are talking about prime numbers.
		Clearly this is not as simple as the basic sieve, but the only major cost is 1 modulus operation for each factor.
	members.tripod.com /~tomwwolf/sieve.htm (681 words)

	The Sieve of Eratosthenes Benchmarks
		The Sieve of Eratosthenes is a standard benchmark used to determine the relative speed of different computers or, in this case, the efficiency of the code generated for the same computer by different compilers.
		The sieve algorithm was developed in ancient Greece and is one of a number of methods used to find prime numbers.
		The sieve works by a process of elimination using an array that starts with 2 and keeps all the numbers in position.
	www.keil.com /benchmarks/sieve.asp (173 words)

	Prime Numbers - Sieve of Eratosthenes :: BlackWasp Software Development
		The Sieve of Eratosthenes algorithm uses a repetitive, manual process to determine a series of prime numbers.
		The Sieve of Eratosthenes is an interesting algorithm but is not perfectly suited to computerisation.
		In the Sieve algorithm, when each prime number is identified, all other numbers that have it as a factor are erased from the list.
	www.blackwasp.co.uk /Eratosthenes.aspx (923 words)

	Alaska Ataca a Kamtchatka: The Genuine Sieve of Eratosthenes
		However, in a feisty paper, Melissa O'Neill clearly shows that this is not the implementation of a sieving process, much less of Eratosthenes's algorithm (see also her rather forceful Haskell Café message).
		As is well-known, Eratosthenes' Sieve begins with an unmarked "grid" (or rather, a list) of integer numbers, starting from 2.
		The downside of using an imperative queue is that we must be mindful of state, and make sure that we start from a known point: we have to prime (!) the sieve with a queue containing just the first known candidate, namely two; from there the process is straightforward.
	alaska-kamtchatka.blogspot.com /2007/12/genuine-sieve-of-eratosthenes.html (1424 words)

	Citations: The segmented sieve of Eratosthenes and primes in arithmetic progressions to - Bays, Hudson (ResearchIndex)
		Carter Bays, Richard H. Hudson, The segmented sieve of Eratosthenes and primes in arithmetic progressions to 10 12, BIT 17 (1977), 121-127.
		Sieving an arithmetic progression is the p adic analogue of sieving a bounded interval.
		The segmented sieve of Eratosthenes and primes in arithmetic progressions to 10 12.
	citeseer.ist.psu.edu /context/60308/0 (902 words)

	Sieve of Eratosthenes
		Sieve of Eratosthenes is an almost mechanical procedure for separating out composite numbers and leaving the primes.
		In order to decide by means of the sieve whether a number such as 9577 is prime, one would have to find all the primes up to 9577.
		There is a variation on the sieve that allows one to do more than sort the natural numbers into two classes.
	science.jrank.org /pages/6147/Sieve-Eratosthenes.html (828 words)

	Fast implementation of the segmented sieve of Eratosthenes
		To do this, the first multiple (belonging to the interval being sieved) of each sieving prime is computed, the subinterval where this multiple lies is identified, and the prime and respective multiple are placed in the appropriate list.
		Since the currently freely available implementations (that I am aware of) of the segmented sieve of Eratosthenes are not very efficient when processing intervals near 10^16 or higher, I have decided to offer a simple implementation of the algorithm.
		Simple implementation [12k, gziped tar archive] of the segmented sieve of Eratosthenes, released under the version 2 (or any later version) of the GNU general public license.
	www.ieeta.pt /~tos/software/prime_sieve.html (1054 words)

	Sieve of Eratosthenes
		When the sieve is shaken the first time the first prime number “2" stays in the sieve and all the multiples of 2 (4, 6, 8,...) fall out through the holes in the sieve.
		The third time the sieve is shaken, the third prime number “5" is held back and lets through all the multiples of 5 that have not already fallen out.
		Each time the sieve is shaken the next prime number is held back and its multiples fall through the mesh.
	educ.queensu.ca /~fmc/december2003/Sieve.html (490 words)

	Sieve of Eratosthenes.
		Eratosthenes (276 -194 B.C.) was a librarian at the great library of Alexandria and was one of the bright guys of the ancient world.
		This particular sieve is built on a 15*35 grid.
		If we wanted to build such a sieve to communicate with extraterrestrials (demonstrating that we know what prime numbers are), we would build a grid with a prime number of squares per side.
	www.egge.net /~savory/maths5.htm (423 words)

	Sieve of Eratosthenes. (Site not responding. Last check: )
		Eratosthenes (276 -194 B.C.) was a librarian at the great library of Alexandria and was one of the bright guys of the ancient world.
		This particular sieve is built on a 15*35 grid.
		If we wanted to build such a sieve to communicate with extraterrestrials (demonstrating that we know what prime numbers are), we would build a grid with a prime number of squares per side.
	home.egge.net /~savory/maths5.htm (423 words)

	Prime Sieve of Eratosthenes - Algorithmist
		The Sieve of Eratosthenes is an algorithm for generating a list of all prime numbers up to a given integer N. It does this using O(N) space and
		The Prime Sieve of Eratosthenes algorithm precalculates from the bottom up - given a table of N values, we "knock off" numbers that can't possibly be a prime - by counting up from hasn't been knocked off.
		This algorithm is usually what is meant when "the sieve of Eratosthenes" is mentioned.
	www.algorithmist.com /index.php/Sieve (557 words)

	Sieve of Eratosthenes Summary and Analysis Summary
		The sieve of Eratosthenes is a useful method for making a list of prime numbers.
		In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer.
		It is the predecessor to the modern Sieve of Atkin, which is faster but more complex.
	www.bookrags.com /Sieve_of_Eratosthenes (193 words)

	Prime Number Sieve/Sieve of Eratosthenes (Site not responding. Last check: )
		The way the usual sieve method works is to find the lowest prime number, and then cross out all multiples of it in the remainder of the list.
		However, the prime N is not lost because it was included and confirmed in the previous Sieve.
		At each step, the next lowest prime number N found by a given sieve is used for the next sieve.
	www.members.aol.com /SciRealm/PrimeSieve.html (1972 words)

	Beacon Lesson Plan Library
		Primed and Ready is a project designed to use the Sieve of Eratosthenes to determine and display the prime and composite numbers from 1 to 100.
		Eratosthenes was interested in the properties of numbers.
		He developed a sieve (a strainer) that allowed the composite numbers from 1 to 100 to fall through, keeping the prime numbers.
	www.beaconlearningcenter.com /Lessons/301.htm (452 words)

	Example Program: The Sieve of Eratosthenes
		An example program that illustrates the use of vectors is the classic algorithm called the sieve of Eratosthenes, used to discover prime numbers.
		In the sieve of Eratosthenes, a list of all the numbers up to some bound is represented by an integer vector.
		The basic idea is to strike out (set to zero) all values that cannot be primes; thus all the remaining values are prime numbers.
	stdcxx.apache.org /doc/stdlibug/5-4.html (225 words)

	Sieve of Eratosthenes
		Eratosthenes of Cyrene (276-194 BC) was the first to estimate accurately the diameter of the earth.
		A sieve is like a strainer that you drain spaghetti through when it is done cooking.
		Proceed to the Sieve of Erathosthenes Applet by Albert Tremblay.
	britton.disted.camosun.bc.ca /jberatosthenes.htm (399 words)

	Sieve of Eratosthenes (Haskell) - LiteratePrograms
		The Sieve of Eratosthenes is an algorithm for rapidly locating all the prime numbers in a certain range of integers.
		This "Sieve of Eratosthenes" is not the genuine algorithm, but is instead a naive version of the original as (incorrectly) taught in most courses on algorithms.
		This code, as stated earlier, is a naive implementation and not an authentic Sieve of Eratosthenes at all.
	en.literateprograms.org /Sieve_of_Eratosthenes_(Haskell) (2435 words)

	Eratosthenes of Cyrene (ca. 284-ca. 192 BC) -- from Eric Weisstein's World of Scientific Biography
		Although most of Eratosthenes' writings are lost, many are preserved through the writings of commentators.
		Among Eratosthenes' accomplishments was the accurate measurement the diameter of the Earth
		Eratosthenes also determined the obliquity of the ecliptic,
	scienceworld.wolfram.com /biography/Eratosthenes.html (207 words)

	Wayne's World of C Code (The Sieve of Eratosthenes)
		I had to develop an instructor solution to a simple C problem, the calculation of primes using the Sieve of Eratosthenes.
		It displayed a message saying that the sieve, which is supposed to contain prime numbers (since to determine primehood you need ONLY to divide by all primes up to one-half the candidate) contained the nonprime number 999!
		Looking at the code I realized I was back in the thrilling days of C and yesteryear, for the code did not appear accidentally to assign an index value to a table entry.
	www.developerdotstar.com /community/node/291/print (965 words)

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