2010733

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=20A002386
• Increasing gaps between prime-powers.at n=25A002540
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=19A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=20A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=21A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=22A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=23A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=24A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=25A079098
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=26A079098
• Smallest prime p such that q = (r-p)/log(p) > n, where r is the next prime after p.at n=9A082891
• 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=21A084974
• Erroneous version of A002540.at n=26A094158
• Smallest prime p(i) such that between 2p(i) and 2p(i+1) there exist n primes.at n=20A104380
• 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=12A111870
• Prime p with prime gap q - p of n-th record Cramer-Shanks-Granville ratio, where q is smallest prime larger than p and C-S-G ratio is (q-p)/(log p)^2.at n=5A111943
• Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime.at n=10A124147
• Primes associated with the prime gaps listed in A085237.at n=37A134266
• Primes prime(n) such that prime(n+1) - prime(n) > log(n)^2.at n=12A182315
• Primes prime(k) corresponding to the records in the sequence (prime(k+1)/prime(k))^k.at n=13A205827