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A236462
Primes p with prime(p) + 4 and prime(p) + 6 both prime.
5
19, 59, 151, 181, 211, 229, 389, 571, 877, 983, 1039, 1259, 1549, 3023, 3121, 3191, 3259, 3517, 3719, 4099, 4261, 4463, 5237, 6947, 7529, 7591, 7927, 7933, 8317, 8389, 8971, 9403, 9619, 10163, 10939, 11131, 11717, 11743, 11839, 12301
OFFSET
1,1
COMMENTS
According to the conjecture in A236460, this sequence should have infinitely many terms.
See A236464 for a similar sequence.
EXAMPLE
a(1) = 19 with 19, prime(19) + 4 = 71 and prime(19) + 6 = 73 all prime.
MATHEMATICA
p[n_]:=p[n]=PrimeQ[Prime[n]+4]&&PrimeQ[Prime[n]+6]
n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10000}]
Select[Prime[Range[1500]], AllTrue[Prime[#]+{4, 6}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 21 2018 *)
PROG
(PARI) s=[]; forprime(p=2, 12500, if(isprime(prime(p)+4) && isprime(prime(p)+6), s=concat(s, p))); s \\ Colin Barker, Jan 26 2014
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 26 2014
STATUS
approved