Definition, Betydelse & Anagram | Engelska ordet PRIMES

Definition av PRIMES

1. böjningsform av prime

Exempel på hur du använder PRIMES i en mening

• Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne primes.
• Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory).
• However, the distribution of primes within the natural numbers in the large can be statistically modelled.
• It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.
• The two primes, p and q, should both be congruent to 3 (mod 4) (this guarantees that each quadratic residue has one square root which is also a quadratic residue), and should be safe primes with a small gcd((p-3)/2, (q-3)/2) (this makes the cycle length large).
• He also showed that the sum of the reciprocals of twin primes converges to a finite value, now called Brun's constant: by contrast, the sum of the reciprocals of all primes is divergent.
• Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger.
• The Meissel–Mertens constant is analogous to the Euler–Mascheroni constant, but the harmonic series sum in its definition is only over the primes rather than over all integers and the logarithm is taken twice, not just once.
• The strong Goldbach conjecture is much more difficult than the weak Goldbach conjecture, which says that every integer (equivalently, every odd integer) greater than 5 is the sum of three primes.
• Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes.
• Once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes.
• Wierzbicka is known for her work in semantics, pragmatics and cross-cultural linguistics, especially for the natural semantic metalanguage and the concept of semantic primes.
• Sophie Germain primes and safe primes have applications in public key cryptography and primality testing.
• Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured that all Fermat numbers are prime.
• In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer.
• In 1937, Ivan Matveevich Vinogradov eliminated the dependency on the generalised Riemann hypothesis and proved directly (see Vinogradov's theorem) that all sufficiently large odd numbers can be expressed as the sum of three primes.
• This is unfortunately false for weak probable primes, because there exist Carmichael numbers; but it is true for more refined notions of probable primality, such as strong probable primes (P = 1/4, Miller–Rabin algorithm), or.
• The German mathematician Peter Gustav Lejeune Dirichlet—for whom the character is named—introduced these functions in his 1837 paper on primes in arithmetic progressions.
• This example is not a sturdy trapdoor function – modern computers can guess all of the possible answers within a second – but this sample problem could be improved by using the product of two much larger primes.
• This sieve is similar to the sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers).

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