A218187 Primes that are the arithmetic mean of 1000 consecutive primes.

82619, 218527, 235811, 265579, 302399, 435661, 594427, 661327, 1007759, 1015499, 1058479, 1134169, 1253047, 1452149, 1492969, 1522799, 1593167, 1593401, 1818293, 1876829, 2007883, 2126429, 2303701, 2341033, 2341643, 2366123, 2433317, 2438629, 2539049, 2547647

Offset: 1

Author

Zak Seidov, Oct 23 2012

Keywords

• nonn

Comments

Subsequence of A123078: a(1) = 82619 = A123078(12), a(2) = 218527 = A123078(30). 302399 is the smallest emirp (A006567) that is the arithmetic mean of 1000 consecutive primes, as 993203 is prime. - Jonathan Vos Post, Oct 25 2012

Examples

			a(1) = 82619 because prime(7569) + ... + prime(8568) = 77017 + ... + 88379 = 82619000.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A123078.

Programs

Mathematica

Select[Mean/@Partition[Prime[Range[400000]],1000,1],PrimeQ] (* Harvey P. Dale, Jul 06 2025 *)