**Question:** What are the currently known best *provable and unconditional* lower and upper bounds for Brun's constant $B$, corresponding to the sum of the reciprocals of the twin primes?


**Remark.** According to Dominic Klyve's thesis "Explicit bounds on twin primes and Brun's Constant" (2007, p.23) the best *provable unconditional* bounds known at the time were given by


$1.830484424658 < B < 2.347$


the lower bound being obtained by computation of the sum up to $10^{16}$. Hence, apparently,


*not even the first digit was known at the time i.e. the question $B<2$ was open.*


Was there any significant progress since then?


Note that the sharper estimates that one usually sees, as that of Nicely


$B=1.90216 05823 \pm 0.00000 00008$


are in fact conjectured but not rigorously proved (95% "confidence interval" according to its author).



Best provable and unconditional lower and upper bounds for Brun's constant
In March 7, 2018 (several months after you asked this question!), Dave Platt and Tim Trudgian published a paper called [Improved bounds on Brun’s constant](https://arxiv.org/pdf/1803.01925.pdf), where they show the following improved bounds:


$$1.840503 < B < 2.288513$$


