31907

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=25A000230
• Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.at n=9A082889
• prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 14.at n=1A109568
• Numbers appearing in A122072 at least four times.at n=19A122390
• Primes p such that q-p = 50, where q is the next prime after p.at n=0A134124
• First occurrence of prime gap 10*n.at n=4A140791
• 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=24A168253
• Primes p such that q*p +- (p mod q) are primes, for q=8.at n=37A178416
• Largest prime all of whose substrings in its base n representation are primes.at n=29A245277
• Primes p such that 2*p^3 + 1 and 2*p^3 + 3 are also primes.at n=22A252042
• a(n) is the least prime p such that the second forward difference of three consecutive primes p, q and r is n = -(p - 2q + r)/2.at n=22A316792
• Primes preceding the first-occurrence gaps in A014320.at n=26A335366
• Numbers k such that there are exactly four biquadratefree powerful numbers (A338325) between k^2 and (k+1)^2.at n=31A338391
• Primes p such that neither g-1 nor g+1 is prime, where g is the gap from p to the next prime.at n=27A355485
• 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=25A363544
• 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=25A368640
• a(n) is the least prime p such that there are exactly n squarefree numbers strictly between p and the next prime, or -1 if there is no such p.at n=30A378111
• Smaller of two consecutive primes p and q, both ending with 7, such that q - p = 10n, or -1 if no such primes exist.at n=4A381510
• Primes which satisfy the requirements of A380943 in more than one way.at n=14A383810
• Primes which satisfy the requirements of A380943 in exactly two ways.at n=13A383811