In spirit of yesterdays post, could the following be true, wild as it is?;

implies

If true, can’t be far from the truth. Do we have ? I very much doubt it.. , and in any case.

EDIT: By just googling “harmonic number 16735” I found some articles from around 1990, that are devoted to exactly this conjecture and it seems like it’s true (it’s proven for all with the possible exception of , and ), but hard. The only remaining conjecture from the previous post seems to hold up too. Anyway, they use p-adic methods, which I am (still) not that familiar with, so I’m definitely going to search for some literature about it.

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