155921

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=43A000230
• 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=14A002386
• Increasing gaps between prime-powers.at n=19A002540
• Primes for which the seven closest primes are smaller.at n=10A075043
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=9A079098
• Smallest prime p such that there is a gap of exactly 2*prime(n) between p and the next prime.at n=13A080082
• 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=13A081413
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=20A082890
• Smallest prime p such that q = (r-p)/log(p) > n, where r is the next prime after p.at n=6A082891
• 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=15A084974
• Erroneous version of A002540.at n=20A094158
• Aloof primes: Total distance between prime and neighboring primes sets record.at n=22A096265
• Smallest prime number that begins a prime gap of at least 2n.at n=36A100964
• Smallest prime number that begins a prime gap of at least 2n.at n=37A100964
• Smallest prime number that begins a prime gap of at least 2n.at n=38A100964
• Smallest prime number that begins a prime gap of at least 2n.at n=39A100964
• 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=8A111870
• Primes where the record gaps in A053686 first appear.at n=7A133788
• Primes associated with the prime gaps listed in A085237.at n=29A134266
• The only primes in single-prime centuries.at n=0A156118