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A137670 Prime numbers p such that p-b < p-a < p < p+a < p+b are prime for some a and b. 0

%I #9 Nov 05 2015 10:49:28

%S 17,23,29,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,

%T 113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,

%U 211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313

%N Prime numbers p such that p-b < p-a < p < p+a < p+b are prime for some a and b.

%C It seems highly likely that all primes other than 2,3,5,7,19 are in this sequence. There are no further exceptions to 4 billion. - _Charles R Greathouse IV_, Apr 19 2010

%t s=""; q=1; For[i=2, i<10^2, p=Prime[i]; For[a=2, a<p, If[PrimeQ[p-a]&&PrimeQ[p+a], For[b=a+2, b<p, If[PrimeQ[p-b]&&PrimeQ[p+b], For[c=b+2, c<p, If[p>q&&PrimeQ[p-c]&&PrimeQ[p+c], (*Print[p, ":", a, ", ", b, ", ", c]; *)s=s<>ToString[p]<>", "; q=p]; c=c+2]]; b=b+2]]; a=a+2]; i++ ]; Print[s]

%Y Cf. A071681.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2008; corrected May 02 2008

%E New name from _Charles R Greathouse IV_, Apr 19 2010

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)