Archiv for Mathematik og Naturvidenskab (in German). 'Über das Goldbachsche Gesetz und die Anzahl der Primzahlpaare'. 'Are all primes (past 2 and 3) of the forms 6 n+1 and 6 n−1?'. UCLA Department of Mathematics – via YouTube. Small and large gaps between the primes (video lecture). Princeton, NJ: Institute for Advanced Study – via ias.edu. 'Yitang Zhang's spectacular mathematical journey'. The ratio of the number of isolated primes less than a given threshold n and the number of all primes less than n tends to 1 as n tends to infinity. It follows from Brun's theorem that almost all primes are isolated in the sense that
In other words, p is not part of a twin prime pair. If m − 4 or m + 6 is also prime then the three primes are called a prime triplet.įor a twin prime pair of the form (6 n − 1, 6 n + 1) for some natural number n > 1, n must end in the digit 0, 2, 3, 5, 7, or 8 ( OEIS: A002822).Īn isolated prime (also known as single prime or non-twin prime) is a prime number p such that neither p − 2 nor p + 2 is prime.
