A309354 Primes of the form p+q+r where p < q < r = p+6 are consecutive primes.

23, 31, 41, 59, 131, 211, 311, 941, 1049, 1381, 1931, 2579, 3271, 3911, 4289, 4451, 4999, 6421, 6719, 8059, 8069, 9769, 10391, 10399, 10589, 11551, 12011, 14369, 16249, 20479, 23269, 23629, 26591, 27031, 28309, 31379, 33349, 33521, 35339, 35491, 39019, 41081

Offset: 1

Author

Philip Mizzi, Jul 25 2019

Keywords

• nonn

Examples

			P = 5 (prime),
P + 2 = 7 (prime),
P + 6 = 11 (prime),
and 5 + 7 + 11 = 23 is prime and is a term.
P = 7 (prime),
P + 4 = 11 (prime),
P + 6 = 13 (prime)
and 7 + 11 + 13 = 31 is prime and is a term.
However, (p,q,r) = (13,17,19) fails because the sum is not a prime.
		

Links

• Eric Weisstein's World of Mathematics, Prime Triplet

Crossrefs

Cf. A098420.

Programs

Mathematica

Select[Total /@ Select[Partition[Prime@Range[2000], 3, 1], #[[3]] == 6 + #[[1]] &], PrimeQ] (* Giovanni Resta, Jul 25 2019 *)

Extensions

More terms from Giovanni Resta, Jul 25 2019