I think they used to explain the formula somewhere or maybe that was LC.

Indeed. The explanation (they provide it in words rather than a mathematical formula) appears several places on their web site, and has not changed in many years.

To calculate Annualized Returns, a total gain or loss is calculated by summing all loan payments received net of principal repayment, credit losses, and servicing costs. The gain or loss is then divided by the average daily amount of principal outstanding to get a simple rate of return. To annualize that rate, we divide it by the dollar-weighted average Note age of your portfolio (calculated in days) and then multiply it by 365. Our Annualized Return calculation includes all Notes issued and sold by Prosper Funding LLC and Prosper Marketplace, Inc. since July 15, 2009

This is actually a pretty straightforward formula. It is identical in spirit to lendingclub's NAR, although there are differences of style. Prosper counts days, whereas LC counts months. Prosper doesn't compound the result, LC does. The two formulas are described differently, so it isn't easy to see immediately that they are the same thing.

The denominator confuses most people, what with the "age" words in there. Its actually pretty simple. The numerator sum contains interest that was earned over a certain number of days, so they divide by that number of days to get a 1 day return, and then multiply by 365 to get an annual return.