Cramér's conjecture and Prime number

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Difference between Cramér's conjecture and Prime number

Cramér's conjecture vs. Prime number

In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Andrica's conjecture

Andrica's conjecture (named after Dorin Andrica) is a conjecture regarding the gaps between prime numbers.

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Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

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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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Heuristic

A heuristic technique (εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.

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Legendre's conjecture

Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between n2 and (n + 1)2 for every positive integer n. The conjecture is one of Landau's problems (1912) on prime numbers;, the conjecture has neither been proved nor disproved.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Prime gap

A prime gap is the difference between two successive prime 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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Riemann hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Twin prime

A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43).

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