44293
domain: N
Properties
Primality
- Prime
- yes
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=29A000230
- Smallest primes whose residue modulo its difference from the next prime is 2n-1.at n=19A060235
- Primes for which the five closest primes are smaller.at n=32A075037
- Primes for which the six closest primes are smaller.at n=11A075038
- Primes for which the seven closest primes are smaller.at n=4A075043
- Primes for which the eight closest primes are smaller.at n=3A075050
- Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=7A079098
- Smallest prime p such that there is a gap of exactly 2*prime(n) between p and the next prime.at n=9A080082
- 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=9A081413
- Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.at n=20A082889
- Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=8A082890
- 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=13A084974
- prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 15.at n=3A109569
- a(n+1) = 3*a(n) - n.at n=11A164039
- 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=28A168253
- Primes p such that q-p = 58, where q is the next prime after p.at n=0A204668
- Primes p(i) such that p(i+1)/p(i) > p(k+1)/p(k) for all k>i, where p(i) is the i-th prime.at n=40A209407
- Primes p followed by a gap of at least 1/2 * log(p)^2.at n=14A211073
- Prime(A215237).at n=5A215238
- 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=8A217724