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As the title says, is it known whether or not the Glaisher constant is a transcendental number?

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Is it known to be irrational? That would perhaps be the first step in the proof. For those who wonder what it is: mathworld.wolfram.com/Glaisher-KinkelinConstant.html – GEdgar Aug 29 '12 at 20:40
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Then there is the conjecture that any naturally generated constant that is not obviously rational or algebraic (by its construction, such as the square root of two) is transcendental. I don't think putting a bounty on this will help. – marty cohen Aug 29 '12 at 22:16

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Math Reviews returns 10 papers when one searches for Glaisher and Kinkelin. Not one of the ten reviews has anything to say about irrationality or transcendence. Absence of evidence is not evidence of absence, but this suggests to me that nothing is known about the question.

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