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39 relations: Algorithm, Analysis of algorithms, Arithmetic progression, Big O notation, Boolean data type, Communications of the ACM, Composite number, Context of computational complexity, Coprime integers, CPU cache, Dataflow programming, David Turner (computer scientist), Divergence of the sum of the reciprocals of the primes, Divisor, Eratosthenes, Functional programming, Greek mathematics, Introduction to Arithmetic, List (abstract data type), Locality of reference, Mathematics, Meissel–Mertens constant, Mertens' theorems, Natural number, Nicomachus, Prime number, Prime number theorem, Prime-counting function, Pseudo-polynomial time, Pseudocode, Random-access machine, Sieve of Atkin, Sieve of Sundaram, Sieve theory, Time complexity, Trial division, Wheel factorization, Wolfram Demonstrations Project, 1.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Analysis of algorithms
In computer science, the analysis of algorithms is the determination of the computational complexity of algorithms, that is the amount of time, storage and/or other resources necessary to execute them.
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Arithmetic progression
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
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Big O notation
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
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Boolean data type
In computer science, the Boolean data type is a data type that has one of two possible values (usually denoted true and false), intended to represent the two truth values of logic and Boolean algebra.
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Communications of the ACM
Communications of the ACM is the monthly journal of the Association for Computing Machinery (ACM).
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Composite number
A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.
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Context of computational complexity
In computational complexity theory and analysis of algorithms, a number of metrics are defined describing the resources, such as time or space, that a machine needs to solve a particular problem.
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Coprime integers
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
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CPU cache
A CPU cache is a hardware cache used by the central processing unit (CPU) of a computer to reduce the average cost (time or energy) to access data from the main memory.
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Dataflow programming
In computer programming, dataflow programming is a programming paradigm that models a program as a directed graph of the data flowing between operations, thus implementing dataflow principles and architecture.
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David Turner (computer scientist)
David A. Turner (born 1946) is a British computer scientist.
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Divergence of the sum of the reciprocals of the primes
The sum of the reciprocals of all prime numbers diverges; that is: This was proved by Leonhard Euler in 1737, and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers.
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Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.
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Eratosthenes
Eratosthenes of Cyrene (Ἐρατοσθένης ὁ Κυρηναῖος,; –) was a Greek mathematician, geographer, poet, astronomer, and music theorist.
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Functional programming
In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data.
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Greek mathematics
Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.
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Introduction to Arithmetic
The book Introduction to Arithmetic (Ἀριθμητικὴ εἰσαγωγή, Arithmetike eisagoge) is the only extant work on mathematics by Nicomachus (60–120 AD).
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List (abstract data type)
In computer science, a list or sequence is an abstract data type that represents a countable number of ordered values, where the same value may occur more than once.
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Locality of reference
In computer science, locality of reference, also known as the principle of locality, is a term for the phenomenon in which the same values, or related storage locations, are frequently accessed, depending on the memory access pattern.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Meissel–Mertens constant
The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as Mertens constant, Kronecker's constant, Hadamard–de la Vallée-Poussin constant or the prime reciprocal constant, is a mathematical constant in number theory, defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm: \sum_ \frac - \ln(\ln n) \right).
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Mertens' theorems
In number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Nicomachus
Nicomachus of Gerasa (Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Prime number theorem
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.
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Prime-counting function
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by (x) (unrelated to the number pi).
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Pseudo-polynomial time
In computational complexity theory, a numeric algorithm runs in pseudo-polynomial time if its running time is a polynomial in the numeric value of the input (the largest integer present in the input) — but not necessarily in the length of the input (the number of bits required to represent it), which is the case for polynomial time algorithms.
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Pseudocode
Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.
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Random-access machine
In computer science, random-access machine (RAM) is an abstract machine in the general class of register machines.
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Sieve of Atkin
In mathematics, the sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer.
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Sieve of Sundaram
In mathematics, the sieve of Sundaram is a simple deterministic algorithm for finding all the prime numbers up to a specified integer.
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Sieve theory
Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Trial division
Trial division is the most laborious but easiest to understand of the integer factorization algorithms.
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Wheel factorization
Wheel factorization is a method for generating lists of mostly prime numbers from a simple mathematical formula and a much smaller list of the first prime numbers.
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Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.
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1
1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.
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Eratosthenes Sieve, Eratosthenes sieve, Eratosthenes' Sieve, Euler's sieve, Net of Eratosthenes, Sieve of Erastosthenes, Sieve of Erastothenes, Sieve of Euler, Sieve of eratosthenes, Κόσκινον Ἐρατοσθένους.
References
[1] https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
