A152127 Sum of cousin primes < 10^n.

28, 766, 325761706602, 1096399967379208796, 542100094312, 41248685420836, 3233516261489332, 260607555289408894, 21446383929686290726, 1795656778320649469818, 152541729206365604807782

Offset

1,1

Comments

"According to the first Hardy-Littlewood conjecture, the cousin primes have the same asymptotic density as the twin primes." See link MathWorld. The (sum of cousin prime pairs < 10^n)/4 ~ number of cousin primes < 10^2n.

Links

Table of n, a(n) for n=1..11.

Cino Hilliard, Gcc Sum of cousin primes

Eric Weisstein's World of Mathematics, Cousin Primes

Formula

Cousin primes are prime pairs that differ by 4. The convention here is to count a cousin pair as long as the first cousin of the pair is less than or equal to the specified bound which in this sequence is 10^n.

Example

(3,7) and (7,11) are the cousin primes < 10. These add up to 28 the first entry in the sequence.

Crossrefs

Sequence in context: A170709 A170747 A218730 * A113532 A158545 A291997

Adjacent sequences: A152124 A152125 A152126 * A152128 A152129 A152130

Keyword

nonn

Author

Cino Hilliard, Nov 25 2008

Status

approved