The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).
Brun's Theorem
See also
Brun's Constant, Twin PrimesExplore with Wolfram|Alpha
References
Brun, V. "La serie
,
les dénominateurs sont nombres premiers jumeaux est convergente où
finie." Bull. Sci. Math. 43, 124-128, 1919.Landau,
E. Elementare
Zahlentheorie. Leipzig, Germany: Hirzel, 1927. Reprinted Providence, RI:
Amer. Math. Soc., 1990.Referenced on Wolfram|Alpha
Brun's TheoremCite this as:
Weisstein, Eric W. "Brun's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrunsTheorem.html