A270203 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12, p+2^14 and p + 2^16 are all primes.

163, 15667, 234067, 607093, 671353, 1447153, 1457857, 2162323, 5772097, 7717873, 9139453, 9549373, 11170933, 12039883, 13243063, 16442407, 16836163, 17784253, 18116473, 19433863, 21960577, 28209703, 29175283, 32380177, 33890803, 34613287, 34682113

Offset

1,1

Links

Dana Jacobsen, Table of n, a(n) for n = 1..10957

Example

The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259, 163 + 16384 = 16547 and 163 + 65536 = 65699 are all primes.

Mathematica

m = {2^4, 2^6, 2^8, 2^10, 2^12, 2^14, 2^16}; Select[Prime@ Range[3*10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)
Select[Prime[Range[22*10^5]], AllTrue[#+2^Range[4, 16, 2], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 12 2018 *)

Prog

(Perl) use ntheory ":all"; say for sieve_prime_cluster(2, 1e8, 16, 64, 256, 1024, 4096, 16384, 65536); # Dana Jacobsen, Jul 13 2016
(Magma) [p: p in PrimesInInterval(2, 40000000) | forall{i: i in [16, 64, 256, 1024, 4096, 16384, 65536] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016

Crossrefs

Subsequence of A269859.

Cf. A269257, A269258, A269259.

Sequence in context: A222837 A134160 A219127 * A049498 A217456 A138932

Adjacent sequences: A270200 A270201 A270202 * A270204 A270205 A270206

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Status

approved