Geodesic
Twin prime statistics
Journal of integer sequences, Tome 8 (2005) no. 4
Hardy and Littlewood conjectured that the the number of twin primes less than $x$ is asymptotic to $2C_2\int_{2}^{x}\frac{dt}{(\log t)^{2}}$ where $C_2$ is the twin prime constant. This has been shown to give excellent results for $x$ up to about $10^{16}$. This article presents statistics supporting the accuracy of the conjecture up to $10^{600}$.
Classification : 11B05, 11A41
Keywords: prime gaps, twin primes, twin prime constant 
@article{JIS_2005__8_4_a0,
     author = {Dubner,  Harvey},
     title = {Twin prime statistics},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {4},
     zbl = {1108.11015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a0/}
}
TY  - JOUR
AU  - Dubner,  Harvey
TI  - Twin prime statistics
JO  - Journal of integer sequences
PY  - 2005
VL  - 8
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a0/
LA  - en
ID  - JIS_2005__8_4_a0
ER  - 
%0 Journal Article
%A Dubner,  Harvey
%T Twin prime statistics
%J Journal of integer sequences
%D 2005
%V 8
%N 4
%U http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a0/
%G en
%F JIS_2005__8_4_a0
Dubner,  Harvey. Twin prime statistics. Journal of integer sequences, Tome 8 (2005) no. 4. http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a0/