134513

Properties

Appears in sequences

• a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.at n=34A000230
• Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.at n=36A046931
• a(n) = Min{ q prime | nextprime(q) - q - 1 = prime(n)}, or 0 if none exist.at n=17A063793
• Primes which can be expressed as sum of distinct powers of 7.at n=5A077721
• a(n) is the smallest prime p of the form 4k+1 such that nextprime(p) - p = 4n.at n=16A082099
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=17A082890
• a(n) is the smallest prime q such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator n (or 0, if such a prime does not exist).at n=33A168253
• Primes of the form abcdabcd..abcdab.at n=30A187114
• Primes whose base-7 representation also is the base-2 representation of a prime.at n=4A235464
• a(n) is the smallest prime p such that the gap between p and the next prime is 4*n.at n=16A301925
• a(n) is the least prime p such that the second forward difference of three consecutive primes p, q and r is n = -(p - 2q + r)/2.at n=31A316792
• Primes preceding the first-occurrence gaps in A014320.at n=34A335366
• Primes p such that the squarefree kernel of the product of the composite numbers between p and the next prime after p (A076978) sets a new record.at n=36A354217
• Primes p such that the number of distinct prime factors omega of the product of the composite numbers between p and the next prime after p sets a new record.at n=26A354219
• a(0) = 2; for n > 0, a(n) is the smallest prime that differs from the next prime by 2n and is not part of a run of 3 or more consecutive primes in arithmetic progression, or -1 if no such prime exists.at n=34A368640
• a(n) is the least prime p such that there are exactly n squarefree numbers strictly between p and the next prime, or -1 if there is no such p.at n=41A378111
• Prime numbersat n=12542