theory, a prime k-tuple is a finite collection of values representing a repeatable pattern of differences between prime numbers. For a k-tuple (a, b, …)...

tends to 1 as n tends to infinity. Cousin prime Prime gap Prime k-tuple Prime quadruplet Prime triplet Sexy prime Thomas, Kelly Devine (Summer 2014). "Yitang...

An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are...

P=(p,p+i_{1},p+i_{2},...,p+i_{k})} denote a prime (k + 1)-tuple, π P ( x ) {\displaystyle \pi _{P}(x)} the number of primes p {\displaystyle p} below x...

Prime quadruplets, quintuplets, and sextuplets are examples of prime constellations, and prime constellations are in turn examples of prime k-tuples....

the asymptotic formula for the number of prime k-tuples less than a given magnitude by generalizing the prime number theorem. It was first proposed by...

Number spiral with 7503 primes visible on regular triangle. Ulam spiral with 10 million primes. Pattern recognition Prime k-tuple Gardner 1964, p. 122....

conjecture and some variants of the prime k-tuple conjecture, that if p > 2 {\displaystyle p>2} is the smallest prime not dividing a {\displaystyle a} ...

formed from prime members of lower order prime k-tuples, 90 is also a record maximal gap between various smaller pairs of prime k-tuples (which include...

distribution of primes. Birkhäuser. pp. 206. ISBN 978-0817644727. Tóth, László (2019), "On The Asymptotic Density Of Prime k-tuples and a Conjecture...

David (2011), Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons, p. 35, ISBN 9781118045718, If the strong prime k-tuples conjecture is...

conjecture on prime k-tuples, and the first violation is expected to likely occur for very large values of x. For example, an admissible k-tuple (or prime constellation)...

n)^{2})} ⁠. Prime gaps can be generalized to prime ⁠ k {\displaystyle k} ⁠-tuples, patterns in the differences among more than two prime numbers. Their...

square of the next prime (11) by > 8. Therefore, for n = 105 {\displaystyle n=105} , n ± 2, ± 4, and ± 8 must be prime (a prime k-tuple). In contrast, n...

lowest-cost path to the goal Admissible prime k-tuple, in number theory regarding possible constellations of prime numbers Admissible set, in mathematical...

Retrieved on 2013-05-06. Tóth, László (2019). "On The Asymptotic Density Of Prime k-tuples and a Conjecture of Hardy and Littlewood" (PDF). Computational Methods...

Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Yalçin (2010). "Primes in Tuples II". Acta Mathematica. 204 (1): 1–47. arXiv:0710.2728. doi:10.1007/s11511-010-0044-9...

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some...

a prime k-tuple, then the function Λ k ( n ; H ) = 1 k ! Λ k ( P H ( n ) ) {\displaystyle \Lambda _{k}(n;{\mathcal {H}})={\frac {1}{k!}}\Lambda _{k}(P_{\mathcal...

mapped to any k-tuple of hash values. In general the polynomial can be evaluated in any finite field. Besides the fields modulo prime, a popular choice...

1215/S0012-7094-41-00826-8. Kourbatov, A. (2013). "Maximal gaps between prime k-tuples: a statistical approach". Journal of Integer Sequences. 16. arXiv:1301...

If 2k + 1 is prime and k > 0, then k itself must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023[update]...

In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem...

factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for...

theory, a Wagstaff prime is a prime number of the form 2 p + 1 3 {\displaystyle {{2^{p}+1} \over 3}} where p is an odd prime. Wagstaff primes are named after...

nonagonal number 1957 = ∑ k = 0 6 6 ! k ! {\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}} = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct...

define the DFT of a ( x ) {\displaystyle a(x)} as the n {\displaystyle n} -tuple ( a ^ j ) = ( a ( ω n j ) ) {\displaystyle ({\hat {a}}_{j})=(a(\omega _{n}^{j}))}...

mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn (i.e. the product of the first n primes). Primality tests...

Hardy–Littlewood prime tuple conjecture) that for any fixed c ≥ 2, the number of representations of a large integer n as the sum of c primes n = p1 + ⋯ +...

In number theory, a Wilson prime is a prime number p {\displaystyle p} such that p 2 {\displaystyle p^{2}} divides ( p − 1 ) ! + 1 {\displaystyle (p-1)...