**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 finner estimates that one usually sees, as that of Nicely

$B=1.90216 05823 +/- 0.00000 00008$

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