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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 25 13:31 EDT 2019. Contains 322461 sequences. (Running on oeis4.)