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of primes has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051) for 
, 2, .... The constant obtained by concatenating these digits
and interpreting them as a binary fraction is therefore
(OEIS A051006).
The continued fraction is [0, 2, 2, 2, 3, 12, 131, 1, ...] (OEIS A051007). It has high-water marks of 0, 2, 3, 12, 131, 169, ... (OEIS A102878), occurring at positions 0, 1, 4, 5, 6, 20, 31, 54, ... (OEIS A103313).
See also
Explore with Wolfram|Alpha
References
Sloane, N. J. A. Sequences A010051, A051006, A051007, A102878, and A103313 in "The On-Line Encyclopedia of Integer Sequences."
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Prime Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrimeConstant.html