83117

Properties

Appears in sequences

• a(n) = smallest prime p = prime(k) such that gcd( prime(k+1) - prime(k), prime(k+2) - prime(k+1) ) is a multiple of 2n.at n=9A054682
• Fourth term of weak prime sextet: p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).at n=28A054831
• Numbers k such that 70^k - 69^k is prime.at n=4A062636
• a(n) = smallest prime p = prime(k) such that gcd( prime(k+1) - prime(k), prime(k+2) - prime(k+1) ) = 2n.at n=9A070018
• Least prime p introducing prime-difference pattern {d, 2*d}, where d = 2*n, i.e., {p, p+2*n, p+2*n+4*n} = {p, p+2*n, p+6*n} are consecutive primes.at n=9A079011
• Primes of the form Sum_{k=1..n} phi(prime(k)).at n=32A101302
• Primes p such that both prevprime(p^2) - 2 and nextprime(p^2) + 2 are also primes.at n=24A226986
• n-th prime that begins with prime(n).at n=22A229206
• Let N(p,i) denote the result of applying "nextprime" i times to p; a(n) = smallest prime p such that N(p,3) - p = 2*n, or -1 if no such prime exists.at n=42A339943
• Prime numbersat n=8118