Talk:Brun's constant

Axel: Brun's constant is denoted as B but Nicely (I don't know why) uses B₂ so I don't see the meaning of change. Please see other references too.
XJamRastafireRootsRockReggaeSecurityInvestigator [2002.02.27] 3 Wednesday somewhere outa space.

Well, you used both B and B₂ in your article, and I decided that one name for the number is enough. If you prefer B, please change it here and also in mathematical constants. AxelBoldt

No need. Let it stay B₂ and let future shows up the decision. Perhaps it would come out that we should name this constant Brun - Hauschaeckell's B_3z constant. Who knows --XJam [2002.02.27] 3 Wednesday (2nd ed.)

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Axel, is this better?

1919 Viggo Brun showed that the sum of the reciprocals of the twin primes (pairs of prime numbers p and q which differ by two) B₂(p,q):

B₂(p,q) = (1/3 + 1/5) + (1/5 + 1/7) + (1/11 + 1/13) + (1/17 + 1/19) + (1/29 + 1/31) + (1/41 + 1/43) + (1/59 + 1/61) + ...

converges to a finite constant now called Brun's constant for twin primes and thus usually denoted by B₂ and defined as:

B₂ = lim_p,q→∞ B₂(p,q).

I think we should 'somehow' distinguish between the sum B₂(p,q) and the Brun's constant B₂.

XJam [2002.04.02] 2 Tuesday (0)

No, your notation is unclear: you write B₂(p,q) for a number that doesn't depend on p and q! Your definition of B₂(p,q) above is exactly Brun's constant; the limit is already built in because of the ... in the formula. It is an infinite series.

I think the definition in the article is clear right now. AxelBoldt, Tuesday, April 2, 2002