Well, to start with, it's called the "prime zeta function" (what a coincidence!). See MathWorld: http://mathworld.wolfram.com/PrimeZetaFunction.html for a start. I don't know anything about your alternating prime zeta function, but the specific sum you mention is A078437; also mentioned in http://mathworld.wolfram.com/PrimeSums.html, equation (7). Franklin T. Adams-Watters -----Original Message----- From: dasimov@earthlink.net Is anything known about (let's dub it) "the prime zeta function" defined for Re(s) > 1 via Pzeta(s) := Sum{n=1..oo} of 1 / (p_n)^s, and elsewhere by analytic continuation, where as usual (p_n)^s := exp(s*ln(p_n)) ??? There's likewise the "alternating prime zeta function" defined for Re(s) > 1 via aPzeta(s) := Sum{n=1..oo} of (-1)^(n+1) / (p_n)^s I wonder what kind of a number aPzeta(1) = 1/2 - 1/3 + 1/5 - 1/7 + 1/11 - 1/13 + . . . = 0.26960+ is. --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.