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In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set of integers. Because it is a simple extension of Eratosthenes' idea, it is sometimes called the Legendre–Eratosthenes sieve.[1]
^Iwaniec, Henryk. The sieve of Eratosthenes–Legendre. Annali della Scuola Normale Superiore di Pisa – Classe di Scienze, Sér. 4, 4 no. 2 (1977), pp. 257–268 MR 453676
mathematics, the Legendresieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes...
Correspondingly, the prototypical example of a sieve is the sieve of Eratosthenes, or the more general Legendresieve. The direct attack on prime numbers using...
prime sieve with reduced real time expended for a given large practical sieving range. Sieve of Eratosthenes LegendresieveSieve of Sundaram Sieve theory...
theorem Brun sieve Function field sieve General number field sieve Large sieve Larger sieve Quadratic sieve Selberg sieveSieve of Atkin Sieve of Eratosthenes...
The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other...
cryptography and the factoring of large numbers. Fermat, Euler, Lagrange, Legendre, and other number theorists of the 17th and 18th centuries established...
construct a perfect number from a Mersenne prime. Another Greek invention, the Sieve of Eratosthenes, is still used to construct lists of primes. Around 1000...
This is the case for small sieves (in particular, some combinatorial sieves such as the Brun sieve) rather than for large sieves; the study of the latter...
ISBN 978-0-19-921986-5. MR 2445243. Zbl 1159.11001. Weintraub, Steven H. (2011). "On Legendre's Work on the Law of Quadratic Reciprocity". The American Mathematical Monthly...
he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such...
In number theory, 1 is the value of Legendre's constant, which was introduced in 1808 by Adrien-Marie Legendre in expressing the asymptotic behavior...
of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special cases. The field of orthogonal polynomials developed...
primes up to n {\displaystyle n} , for instance using the sieve of Eratosthenes, and uses Legendre's formula to compute the exponent for each prime. Then it...
cases can be combined into a single, non-piecewise formula, using the Legendre symbol: p ∣ F p − ( 5 p ) . {\displaystyle p\mid F_{p\;-\,\left({\frac...
known as the asymptotic law of distribution of prime numbers. Adrien-Marie Legendre conjectured in 1797 or 1798 that π(a) is approximated by the function a/(A...
test Lucas primality test Miller–Rabin primality test Sieve of Atkin Sieve of Eratosthenes Sieve of Sundaram Euler method Backward Euler method Trapezoidal...
written as a sum of at most four hexagonal numbers is 130. Adrien-Marie Legendre proved in 1830 that any integer greater than 1791 can be expressed in this...
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