Ask HN: Tiny single-board computers with Bluetooth and multi-day battery power?

I have an idea in the field of mesh networking, but it would require some specialized hardware. Are there any single-board computers that are credit card size or smaller, feature Bluetooth antennas that could reach across a room, and would (theoretically) be able to run off a D battery for at least a couple of days? Might be a stretch, but it seems that Apple's Airpods are already mostly there. Is there anything along these lines that I could get off the shelf? Thank you!