404597

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=37A000230
• a(n) = Min{ q prime | nextprime(q) - q - 1 = prime(n)}, or 0 if none exist.at n=19A063793
• n*10^7-1, n*10^7-3, n*10^7-7 and n*10^7-9 are all prime.at n=18A064982
• Smallest prime p such that there is a gap of exactly 2*prime(n) between p and the next prime.at n=11A080082
• 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=11A081413
• Increasing peaks in the prime gap sequence A000230.at n=8A086977
• 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=13A109569
• Records in A000230.at n=19A133429
• a(n) is the smallest prime q > a(n-1) such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator prime(n) (or 0, if such a prime does not exist).at n=11A179328
• Least prime such that between it and the next prime there are exactly n semiprimes.at n=24A228171
• Primes P where the nearest prime is greater than 3*log(P) away.at n=15A330427
• Least prime p such that 2n can be written as the sum or absolute difference of p and the next prime, or -1 if no such prime exists.at n=37A363544
• a(0) = 2; for n > 0, a(n) is the smallest prime that differs from the next prime by 2n and is not part of a run of 3 or more consecutive primes in arithmetic progression, or -1 if no such prime exists.at n=37A368640
• Prime numbersat n=34202