A152127 Sum of cousin primes < 10^n.

28, 766, 34522, 1706602, 107863996, 7379208796, 542100094312, 41248685420836, 3233516261489332, 260607555289408894, 21446383929686290726, 1795656778320649469818, 152541729206417144415334, 13119208549320820341969112, 1140316445909100202181666752

Offset

1,1

Comments

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.

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

Links

Benjamin Chaffin, Table of n, a(n) for n = 1..19

Cino Hilliard, Gcc Sum of cousin primes. [broken link]

Eric Weisstein's World of Mathematics, Cousin Primes.

Example

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

Prog

(PARI) lista(pmax) = {my(sm = 10, prev = 2, pow = 10); forprime(p = 3, pmax, if(p == prev + 4, sm += (prev + p)); if(p > pow, print1(sm, ", "); pow *= 10); prev = p); } \\ Amiram Eldar, Jul 06 2024

Crossrefs

Cf. A023200, A046132, A080840, A152052.

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

Extensions

Data corrected by Amiram Eldar, Jul 06 2024

a(13) corrected by and a(14)-a(15) from Benjamin Chaffin, Jun 02 2026

Status

approved