41603

Properties

Appears in sequences

• Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[6, 2,6]; short d-string notation of pattern = [626].at n=30A078854
• Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,4).at n=10A078959
• Numbers p such that p = (prime(n)+ prime(n+2))/2 is prime for prime indices n=2, 3, 5...at n=35A098038
• Primes of the form n^2 - 13.at n=19A154648
• Primes p such that p^2 - 8, p^2 - 6 and p^2 - 2 are prime.at n=16A176960
• Primes p such that p - d and p + d are also primes, where d is the largest digit of p.at n=26A245877
• Primes p such that 2*p^2 + 3 and 2*p^2 + 5 are also primes.at n=29A247197
• Primes whose trajectories under the map x -> A039951(x) enter the cycle {83, 4871} (conjectured).at n=9A252812
• Least prime p such that prime(p*n)-1 is a square, or 0 if no such p exists.at n=33A259764
• Centered 22-gonal primes.at n=26A276262
• Sophie Germain primes p such that p+6 and p-6 are primes.at n=34A278869
• Primes for which the sum of all preceding odd-indexed prime gaps is exactly one greater than the sum of all preceding even-indexed prime gaps.at n=26A282178
• Union of 2, A282178, and A330339.at n=36A330554
• a(n) is the least prime p = prime(k) such that the next prime with the same last digit as p is prime(k+n).at n=21A340800
• Primes p such that (p^128 + 1)/2 is prime.at n=26A341230
• G.f. A(x) satisfies: A(x) = P(x)/Q(x) where P(x) = Sum_{n>=0} (n+1)*x^n*A(x)^(3*n)/(1 - x*A(x)^(n+1))^2 and Q(x) = Sum_{n>=0} (n+1)*x^n*A(x)^(2*n)/(1 - x*A(x)^(n+2)).at n=7A341320
• a(n) = (a(n-3)*a(n-9) + a(n-1)*a(n-11))/a(n-12) with a(0) = ... = a(11) = 1.at n=29A375922
• Prime numbersat n=4350