Legendre's conjecture oor Spaans
Legendre's conjecture
en
A prime number between n2 and (n+1)2 exists for every positive integer n.
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conjetura de Legendre
en
A prime number between n2 and (n+1)2 exists for every positive integer n.
es
Existe un número primo entre n al cuadrado y su sucesor al cuadrado para cada entero positivo n.
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Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares?
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His work on the twin prime conjecture, Waring's problem, Goldbach's conjecture and Legendre's conjecture led to progress in analytic number theory.
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Legendre's conjecture that there is a prime between consecutive integer squares directly implies that there are at least two primes between prime squares for pn ≥ 3 since pn+1 - pn ≥ 2.
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In 1915, 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 as Goldbach's conjecture and the twin prime conjecture.
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At the start of the 19th century, Legendre and Gauss independently conjectured that as x tends to infinity, the number of primes up to x is asymptotic to x/ln(x), where ln(x) is the natural logarithm of x.
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In "Eléments" Legendre gave a simple proof that is irrational, as well as the first proof that is irrational, and conjectured that is not the root of any algebraic equation of finite degree with rational coefficients.
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6 sinne gevind in 3 ms. Hulle kom uit baie bronne en word nie nagegaan nie.