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Decimal expansion of the real part of the complex zero of the Prime Zeta function nearest the point {0,0}.
3

%I #22 Dec 07 2022 09:43:37

%S 2,5,3,7,5,1,6,1,0,0,3,7,5,4,1,1,1,6,9,2,5,0,6,6,8,0,1,0,3,9,2,2,8,3,

%T 1,6,0,7,6,2,9,6,5,6,9,4,1,6,6,6,5,0,0,0,0,2,9,5,7,5,7,5,2,9,7,5,8,5,

%U 6,7,0,7,5,7,9,3,8,1,0,9,2,4,3,2,6,6,1,9,9,1,5,2,0,3,9,6,9,1,6,9,8,5,5,4,3,2,5,9,9,7,6,4,7,0,0

%N Decimal expansion of the real part of the complex zero of the Prime Zeta function nearest the point {0,0}.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>

%e P(0.253751610037541116925066801039228316076296569416665... + i*4.7581147960914060941595212380426498512150296376740568185876345...) = 0.

%t Re[z /. FindRoot[PrimeZetaP[z] == If[$VersionNumber < 12.3, 0, 2*Pi*I], {z, 1/4 + 5*I}, WorkingPrecision -> 120]] (* _Vaclav Kotesovec_, Dec 07 2022 *)

%Y Cf. A358924.

%K nonn,cons

%O 0,1

%A _Artur Jasinski_, Dec 06 2022