Viggo Brun's Constant

So, I was reading this article: Easy as pi: how Google bid against Apple and Microsoft for patents and at one point it mentions Brun's Constant.  Off to Wikipedia and I find that is defined as the sum of the reciprocals of all of the twin primes.  (See: Brun's Theorem.)  Here's a screen shot of the equation since I don't know how to do all the fancy formatting to type it out myself.

Then according to Thomas R. Nicely's Enumeration to 1.6e15 of the twin primes and Brun's constant article this converges to 1.90216 05824 +/- 0.00000 00030 and he states that represents a 99% confidence level.  Mr. Nicely also clarifies that the validity of the Hardy-Littlewood approximation of the twin prime conjecture is central to his estimation of Brun's constant.  (If I'm understanding it right.)

Anywho, what I noticed is the value of Brun's constant is eerily similar to the 9th root of 326 which is 1.90215 71760 (to the same number of decimal places) and that is 99.9998209% of the calculated value for Brun's constant.

All that to say: Jessie's conjecture, based on nothing more than what would look pretty, is that Brun's constant should be equal to the 9th root of 326.  Or perhaps the 17th root of 55,873 which is an even closer match.  Then again the 29th root of 125,362,647 gets closer still.  It being 99.9999999% of Nicely's approximation.  Is there any correlation here?  I dunno.

Next I got sidetracked by reading about Brun's constant for prime quadruplets and the Enumeration to 1.6e15 of the prime quadruplets article shows Mr. Nicely's calculation for that as 0.87058 83800 +/- 0.00000 00005 which is quite similar to the 5th root of 0.5 at 0.87055 05633 (to the same number of decimal places).  This is 99.9956562% of that number.  Coincidence again?

BTW, here is a fun site to play around at: WolframAlpha.  Click on examples to get started.