A127270 Primes prime(k) such that the sum of the composites between prime(k) and prime(k+2) is prime.
19, 79, 229, 271, 349, 359, 373, 677, 733, 743, 751, 797, 937, 1231, 1279, 1459, 1489, 1549, 1733, 1789, 1801, 1973, 1979, 2069, 2539, 2693, 2777, 2791, 2837, 2857, 3061, 3083, 3191, 3329, 3557, 3559, 3659, 3691, 3719, 3919, 3929, 3989, 4129, 4283, 4447
Offset: 1
Keywords
Examples
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.
Programs
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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 */
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Mathematica
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 *)
Extensions
Edited and extended by Klaus Brockhaus, Mar 29 2007