1357201

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=19A002386
• Increasing gaps between prime-powers.at n=24A002540
• Smallest prime p such that there is a gap of 6n between p and the next prime.at n=21A058193
• a(n) = Min{ q prime | nextprime(q) - q - 1 = prime(n)}, or 0 if none exist.at n=30A063793
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=17A079098
• Smallest prime p such that q = (r-p)/log(p) > n, where r is the next prime after p.at n=8A082891
• Primes that show the slow decrease in the larger values of the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime.at n=19A084974
• Erroneous version of A002540.at n=25A094158
• Aloof primes: Total distance between prime and neighboring primes sets record.at n=26A096265
• Prime p with prime gap q - p of n-th record merit, where q is smallest prime larger than p and the merit of a prime gap is (q-p)/log(p).at n=11A111870
• Primes where the record gaps in A053686 first appear.at n=8A133788
• Primes associated with the prime gaps listed in A085237.at n=35A134266
• The only primes in single-prime centuries.at n=7A156118
• Primes prime(k) corresponding to the records in the sequence (prime(k+1)/prime(k))^k.at n=12A205827
• First prime in A122072 that appears at least n times.at n=12A206473
• Primes p followed by a gap of at least 1/2 * log(p)^2.at n=34A211073
• Prime(A215237).at n=9A215238
• Smallest number requiring n steps to reach a prime under the "add a digit" process described in A241180.at n=17A241182
• a(n) = smallest prime p such that there is a gap of n*(n+1) between p and the next prime.at n=10A241886
• Primes p such that the next prime appears after a gap greater than 100.at n=4A252800