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It is well known that the sum of all inverse primes is divergent. But the alternating sum is convergent by the Leiniz criterion. To which known constant "a" does the sum converge?

$$a = \frac{1}{2} - \frac{1}{3} +\frac{1}{5}-\frac{1}{7}+\frac{1}{11} -+ ...$$

Dr. Wolfgang Hintze
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    your wording implies that the answer is known, if not to you, then someone. My guess would be that nobody knows. – Will Jagy Aug 06 '18 at 20:32
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    You will see an answer here : https://math.stackexchange.com/questions/241728/convergence-of-alternating-series-based-on-prime-numbers – Pjonin Aug 06 '18 at 20:33
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    @gimusi I have looked at the proposed answer. It deals with the convergence only, which, as I said in my post is granted by the Leibniz criterion. My question asks if the limit is a known constant, or can be expressed by known constants. – Dr. Wolfgang Hintze Aug 06 '18 at 20:42
  • https://oeis.org/A078437 Only the first few digits are known. All currently known digits: $0.26960635197167\dots$ – JMoravitz Aug 06 '18 at 20:43
  • @Dr.WolfgangHintze Look at the third answer https://math.stackexchange.com/a/2329044/505767 – user Aug 06 '18 at 20:43
  • @gomusi I have found hint to a - negative - answer to my question following the comment of Pjonin here. – Dr. Wolfgang Hintze Aug 06 '18 at 20:57

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For clarity and completeness, I have put the information in the comments into an answer...

As mentioned, this series has an expansion given by the OEIS, which states that the most accurate known estimate of the limit is 0.26960635197167...

The references given therein, as well as others such as Mathworld, Wells, Robinson & Potter and Weisstein indicate that no known closed form of this limit is known, nor does it have its own special name or symbol.

Martin Roberts
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    Thank you for your clarifying contribution. This answers my question in the sense that the result of the sum has no name. The duplicate announcement is wrong, however, since the provided link does NOT give an answer to my question. I have explained this clearly in a comment, and I refrain from repeating myself. – Dr. Wolfgang Hintze Aug 07 '18 at 15:13