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A108117
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Numbers n such that prime(k)*n+prime(k+1), for k=1,...,7 all are primes.
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0
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3494, 60674, 75494, 1122584, 2136044, 2473934, 3367244, 5600384, 6629804, 6910784, 7554644, 8572904
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OFFSET
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1,1
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COMMENTS
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The only n, for which also 19*3494+23 is prime, is n=5600384. In principle, n == 4 (mod 10) can give primes of the form prime(k)*n+prime{k+1), for all k from 1 up to 41, while prime(42)*4+prime(43)=181*4+191 == 5 (mod 10) that is nonprime. It'd be very interesting to find at least one n such that prime[k]*n+prime[k+1), k=1,...,41 are all prime.
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LINKS
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Table of n, a(n) for n=1..12.
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EXAMPLE
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3494 is OK because 2*3494+3, 3*3494+5, 5*3494+7, 7*3494+11, 11*3494+13, 13*3494+17 and 17*3494+19 all are primes.
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MATHEMATICA
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s={}; Do[If[Union[PrimeQ/@Table[Prime[k]*n+Prime[k+1], {k, 7}]]=={True}, s=Append[s, n]], {n, 4, 10000000, 10}]; s
Select[Range[9*10^6], AllTrue[Prime[Range[7]]#+Prime[Range[2, 8]], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 24 2018 *)
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CROSSREFS
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Sequence in context: A204960 A249525 A252049 * A233992 A203845 A257316
Adjacent sequences: A108114 A108115 A108116 * A108118 A108119 A108120
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov, Jun 03 2005
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STATUS
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approved
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