commonly written as ln(x) or loge(x). A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn or g(pn) is the difference...

However, large prime gaps occur much earlier than this argument shows. For example, the first prime gap of length 8 is between the primes 89 and 97, much...

prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin...

definitions. Primes with equal-sized prime gaps after and before them, so that they are equal to the arithmetic mean of the nearest primes after and before...

length of this gap is asymptotically smaller than the average composite run for integers of similar size (see prime gap). Primorial prime Weisstein, Eric...

integer not greater than N is prime is very close to 1 / log(N). In other words, the average gap between consecutive prime numbers among the first N integers...

2. The prime number theorem implies that on average, the gap between the prime p and its successor is log p. However, some gaps between primes may be...

different proof of Yitang Zhang's theorem that there are bounded gaps between primes, and resolved a longstanding conjecture by showing that for any m...

2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. This work led to a 2013 Ostrowski...

infinitely many primes p (later called Chen primes) such that p + 2 is either a prime or a semiprime. It suffices to check that each prime gap starting at...

is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture...

Archived from the original on 18 January 2011. Retrieved 16 July 2020. "Prime Gap Grows After Decades-Long Lull". 10 December 2014./ KEVIN HARTNETT (5 June...

981 = Starts the first prime gap sequence of 2, 4, 6, 8, 10, 12, 14 129,106 = Keith number 130,321 = 194 131,071 = Mersenne prime 131,072 = 217 and largest...

were testing contains the largest known relative gap between Mersenne primes: the next Mersenne prime exponent, 521, would turn out to be more than four...

Friedman prime 15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples (in between which lies a record prime gap of...

balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and...

BBS cultures. 31395 = square pyramidal number 31397 = prime number followed by a record prime gap of 72, the first greater than 52 31688 = the number of...

1 ) {\displaystyle a(n-1)} with a prime number p {\displaystyle p} , the smallest prime whose following prime gap is larger than a ( n − 1 ) {\displaystyle...

Confederation, there were gaps between the term of an outgoing prime minister and the incoming prime minister. The shortest gap, two days, was between Macdonald...

Pine Gap is a joint Australian–United States satellite communications and signals intelligence surveillance base and Australian Earth station approximately...

A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers...

conjectures related to prime gaps, that is, to the spacing between prime numbers. Others include Bertrand's postulate, on the existence of a prime between n {\displaystyle...

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 January 2025[update]...

sum of primes (and 1) using each at most once. The only harmonic number that is an integer is the number 1. Oppermann's conjecture Prime gap Proof of...

Closing the Gap: The Quest to Understand Prime Numbers is a book on prime numbers and prime gaps by Vicky Neale, published in 2017 by the Oxford University...

difference of prime squares 1361 = first prime following a prime gap of 34, centered decagonal number, 3rd Mills' prime, Honaker prime 1362 = number of...

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...

infinitely many Woodall primes? More unsolved problems in mathematics Woodall numbers that are also prime numbers are called Woodall primes; the first few exponents...

Romanian mathematician Dorin Andrica (es)) is a conjecture regarding the gaps between prime numbers. The conjecture states that the inequality p n + 1 − p n <...

conjecture has been verified for all primes below 264 ≈ 1.84×1019. If the conjecture were true, then the prime gap function g n = p n + 1 − p n {\displaystyle...