31397

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=36A000230
• 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=13A002386
• Increasing gaps between prime-powers.at n=18A002540
• Lower prime of a record difference between it and the second prime after it.at n=18A031133
• Primes reached in A037271, or -1 if no such prime exists.at n=21A037272
• Home primes: for n >= 2, a(n) = the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached (a(n) = -1 if no prime is ever reached).at n=33A037274
• Trajectory of 34 under prime factor concatenation procedure.at n=13A037933
• Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.at n=37A046931
• Largest n-digit prime at the start of a record in the RECORDS transform of the prime gaps.at n=4A053302
• Smallest prime p such that there is a gap of 6n between p and the next prime.at n=11A058193
• a(n) = Min{ q prime | nextprime(q) - q - 1 = prime(n)}, or 0 if none exist.at n=18A063793
• Primes of form p = 2 + Sum_{k = 1..m} k^2 for some m.at n=10A065244
• Smaller of pair of successive n-digit primes with maximal difference.at n=4A073861
• Primes for which the five closest primes are smaller.at n=19A075037
• Primes for which the six closest primes are smaller.at n=6A075038
• Primes for which the seven closest primes are smaller.at n=2A075043
• Primes for which the eight closest primes are smaller.at n=1A075050
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=4A079098
• a(n) is the smallest prime p of the form 4k+1 such that nextprime(p) - p = 4n.at n=17A082099
• Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.at n=8A082889