A058620 Lesser of two consecutive primes whose difference divided by two is a prime: ( prime(next prime after n) - prime(n) )/2 is prime.

7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 97, 103, 109, 113, 127, 131, 139, 151, 157, 163, 167, 173, 181, 193, 223, 229, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 313, 317, 331, 337, 349, 353, 367, 373, 379, 383, 397, 409, 421, 433, 439

Offset: 1

Author

Robert G. Wilson v, Dec 28 2000

Keywords

• nonn

Comments

Lesser of two consecutive primes whose difference is a semiprime (A001358). - Zak Seidov, Nov 19 2016

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358.

Programs

Mathematica

Do[ If[ PrimeQ[ (Prime[n + 1] - Prime[n] )/2], Print[ Prime[n] ]], {n, 1, 100} ]
p=7;Reap[Do[If[PrimeQ[((q=NextPrime[p])-p)/2],Sow[p]];p=q,{100}]][[2, 1]] (* Zak Seidov, Nov 19 2016 *)
Select[Partition[Prime[Range[100]],2,1],PrimeQ[(#[[2]]-#[[1]])/2]&][[All,1]] (* Harvey P. Dale, Jan 20 2021 *)

PARI

isok(p) = isprime(p) && isprime((nextprime(p+1) - p)/2); \\ Michel Marcus, Nov 19 2016

PARI

v=List(); p=3; forprime(q=5,, if(isprime((q-p)/2), listput(v,p); if(#v==10^4, return)); p=q) \\ Charles R Greathouse IV, Nov 20 2016