A370139 Primes p such that the sums of three, five, and seven consecutive primes starting with p are prime.

19, 29, 31, 53, 79, 379, 401, 839, 883, 1301, 1409, 1951, 1973, 2113, 2683, 2791, 2833, 3407, 3613, 3793, 3823, 4441, 4751, 4831, 5623, 5827, 6133, 6329, 7187, 7237, 7703, 8527, 9173, 10103, 10853, 11317, 12277, 13163, 13933, 14159, 14827, 15241, 15667

Offset: 1

Author

Harvey P. Dale, Feb 11 2024

Keywords

• nonn

Examples

			379 is in the sequence because the seven consecutive primes starting with 379 are 379, 383, 389, 397, 401, 409, and 419, and (379+383+389)=1151, and (379+383+389+397+401)=1949, and (379+383+389+397+401+409+419)=2777, and 1151 and 1949 and 2777 are all primes.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A180948 and A182121.

Programs

Mathematica

Select[Partition[Prime[Range[5000]],7,1],AllTrue[{Total[Take[#,3]],Total[Take[#,5]],Total[#]},PrimeQ]&][[;;,1]]