In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression...

are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there are infinitely many primes that are congruent...

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains...

arbitrarily long arithmetic progressions. In other words, for every natural number k {\displaystyle k} , there exist arithmetic progressions of primes with k {\displaystyle...

Erdős–Selberg argument". Let πd,a(x) denote the number of primes in the arithmetic progression a, a + d, a + 2d, a + 3d, ... that are less than x. Dirichlet...

finite arithmetic progressions, of any arbitrary length k. Erdős made a more general conjecture from which it would follow that The sequence of primes numbers...

product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural...

positive integers by taking as a base a suitable collection of arithmetic progressions, sequences of the form { b , b + a , b + 2 a , . . . } {\displaystyle...

public advocacy group based in Washington, D.C. Consecutive primes in arithmetic progression, a mathematical term relating to prime number series C/PAP, a...

primes. One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes...

The AP27 is listed in "Jens Kruse Andersen's Primes in Arithmetic Progression Records page". Rowland, Eric S. (2008), "A Natural Prime-Generating Recurrence"...

balanced primes. Three consecutive primes in arithmetic progression is sometimes called a CPAP-3. A balanced prime is by definition the second prime in a CPAP-3...

Belphegor's prime, and primes in arithmetic progression. In 1993 he was responsible for more than half the known primes of more than two thousand digits...

In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications...

in the OEIS) One of PrimeGrid projects was AP26 Search which searched for a record 26 primes in arithmetic progression. The search was successful in April...

positive c and L such that, if we denote p(a,d) the least prime in the arithmetic progression a + n d ,   {\displaystyle a+nd,\ } where n runs through...

largest primes, but unlike the breakthrough of Ben J. Green and Terence Tao – the Green–Tao theorem, that there are arithmetic progressions of primes of arbitrary...

in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. Additive number theory is concerned...

(April 1949). "An Elementary Proof of Dirichlet's Theorem About Primes in Arithmetic Progression". Annals of Mathematics. 50 (2): 297–304. doi:10.2307/1969454...

in the distribution of primes in arithmetic progressions, and he coined the term "prime number race" for irregularities in the distribution of prime numbers...

special importance in the Chabad-Lubavitch Hasidic movement. 771 = 3 × 257, sum of three consecutive primes in arithmetic progression (251 + 257 + 263)...

triplet, (65537, 65539, 65543); a middle member of a three-term primes in arithmetic progression, (65521, 65539, 65557). 65,792 = Leyland number using 2 & 16...

event in Western Australia PAP-k, k primes in arithmetic progression in mathematics Post-activation potentiation, a physiological response utilized in sports...

In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured...

Dirichlet who introduced them in (Dirichlet 1837) to prove the theorem on primes in arithmetic progressions that also bears his name. In the course of the proof...

Schinzel's hypothesis H. Prime triplet Green–Tao theorem First Hardy–Littlewood conjecture Prime constellation Primes in arithmetic progression Dickson, L. E. (1904)...

prime. The special case when the polynomials are m, 2m, ..., km implies the previous result that there are length k arithmetic progressions of primes...

distribution of primes in arithmetic progressions, averaged over a range of moduli. The first result of this kind was obtained by Mark Barban in 1961 and the...

Russian). 12 (1): 57–78. Heath-Brown, D. R. (May 1978). "Almost-primes in arithmetic progressions and short intervals". Mathematical Proceedings of the Cambridge...

3. "Prime number information". mathworld.wolfram.com. Sloane, N. J. A. (ed.). "Sequence A007510 (Single (or isolated or non-twin) primes: Primes p such...