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A270203
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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.
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4
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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