1349533

Properties

Appears in sequences

• Primes (lower end) with record gaps to the next consecutive prime: primes p(k) where p(k+1) - p(k) exceeds p(j+1) - p(j) for all j < k.at n=18A002386
• Increasing gaps between prime-powers.at n=23A002540
• Smallest prime p such that there is a gap of exactly 2*prime(n) between p and the next prime.at n=16A080082
• a(n) is the smallest prime p such that the largest prime divisor of the difference nextprime(p) - p equals the n-th prime, prime(n).at n=16A081413
• Middle q of three consecutive primes p,q,r, such that one adjacent prime is near, the other is far and the ratio of the differences (whichever of (r-q)/(q-p) or (q-p)/(r-q) is greater than 1) sets a record.at n=20A084105
• Erroneous version of A002540.at n=24A094158
• Primes associated with the prime gaps listed in A085237.at n=34A134266
• First prime in A122072 that appears at least n times.at n=11A206473
• Primes p followed by a gap of at least 1/2 * log(p)^2.at n=33A211073
• Smallest prime producing a gap with the next prime, the size of the gap being a composite number with 2n+1 as a factor.at n=18A217724
• Primes p such that the next prime appears after a gap greater than 100.at n=3A252800
• a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)/3) sets a new record.at n=16A337489
• a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime, but prime(n+1) does not divide any of these.at n=38A341640
• Primes preceding record runs of composites coprime to 30 (A007775).at n=14A348394
• 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=44A354217
• 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=32A354219
• a(n) = smallest prime Q of a consecutive prime triple {P, Q, R} such that floor( (R-Q) * (Q-P) / 8 ) = n.at n=28A375009
• Primes p such that the difference between the average of the next 2 primes after p and p sets a new record.at n=26A375095
• Smallest prime p where the absolute difference of the gaps to the adjacent primes exceeds n*log(p).at n=7A383591
• Prime numbersat n=103520