89689

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=32A000230
• Smallest prime p such that there is a gap of 2^n between p and the next prime.at n=6A062529
• a(1) = 2; for n > 1, a(n) is the smallest prime > a(n-1) such that each successive digit in the concatenation of terms (that does not follow 9) is greater than the previous digit.at n=24A068827
• Primes for which the six closest primes are smaller.at n=22A075038
• Primes for which the seven closest primes are smaller.at n=6A075043
• Primes for which the eight closest primes are smaller.at n=4A075050
• a(n) is the smallest prime p of the form 4k+1 such that nextprime(p) - p = 4n.at n=15A082099
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=12A082890
• Let a(1)=1; for n>1, a(n)=nextprime( a(n-1)^(n/(n-1)) ).at n=20A084573
• Primes with digit sum = 40.at n=13A106773
• Every digit of prime and its index contains a loop (only digits 0,4,6,8,9 in prime and its index).at n=13A107625
• 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=5A109569
• First occurrence of prime gaps which are perfect powers.at n=6A123995
• Records in A000230.at n=16A133429
• First occurrence of prime gaps which are squares.at n=4A138198
• Primes p such that q-p = 64, where q is the next prime after p.at n=0A204670
• 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=9A217724
• Primes with integer arithmetic mean of digits = 8 in base 10.at n=20A285228
• a(n) is the smallest prime p such that the gap between p and the next prime is 4*n.at n=15A301925
• Primes preceding the first-occurrence gaps in A014320.at n=33A335366