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%I #12 Feb 28 2023 03:28:00
%S 19,79,229,271,349,359,373,677,733,743,751,797,937,1231,1279,1459,
%T 1489,1549,1733,1789,1801,1973,1979,2069,2539,2693,2777,2791,2837,
%U 2857,3061,3083,3191,3329,3557,3559,3659,3691,3719,3919,3929,3989,4129,4283,4447
%N Primes prime(k) such that the sum of the composites between prime(k) and prime(k+2) is prime.
%e The composites between prime(8) = 19 and prime(10) = 29 are 20, 21, 22, 24, 25, 26, 27, 28. Their sum 193 is prime, hence prime(8) = 19 is a term.
%t Do[p = Prime[n]; If[PrimeQ[Apply[Plus, Select[Table[i, {i, p + 1, Prime[n + 2] - 1}], Not[PrimeQ[ # ]] &]]], Print[p]], {n, 1, 1000}] (* _Michael Taktikos_, Apr 01 2007 *)
%o (Magma) [ p: p in [ NthPrime(k): k in [1..650] ] | IsPrime(&+[ c: c in [p+1..NextPrime(NextPrime(p))-1] ] - NextPrime(p)) ]; /* _Klaus Brockhaus_, Mar 29 2007 */
%K nonn
%O 1,1
%A _J. M. Bergot_, Mar 27 2007
%E Edited and extended by _Klaus Brockhaus_, Mar 29 2007
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