A236481 Primes p with p + 2, prime(p) + 2 and prime(prime(p)) + 2 all prime.

3, 1949, 4217, 8219, 9929, 22091, 23537, 28097, 38711, 41609, 50051, 60899, 68111, 72227, 74159, 79631, 115151, 122399, 127679, 150959, 155537, 266687, 267611, 270551, 271499, 284741, 306347, 428297, 433661, 444287

Offset: 1

Author

Zhi-Wei Sun, Jan 26 2014

Keywords

• nonn

Comments

Conjecture: For any positive integer m, there are infinitely many chains p(1) < p(2) < ... < p(m) of m primes with p(k) + 2 prime for all k = 1,...,m such that p(k + 1) = prime(p(k)) for every 0 < k < m.

Examples

			a(1) = 3 since 3, 3 + 2 = 5, prime(3) + 2 = 7 and prime(prime(3)) + 2 = prime(5) + 2 = 13 are all prime, but 2 + 2 = 4 is composite.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..5000
• Zhi-Wei Sun, A new kind of prime chains, a message to Number Theory List, Jan. 20, 2014.

Crossrefs

Cf. A000010, A000040, A001359, A006512, A235925, A236066, A236457, A236458, A236468, A236470, A236480, A236482, A236484.

Programs

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10^6}]