I previously did tests of the probability of repeating bits 1111x and 0000x on a range of 256 bits. To do this I generated 100 million urandom(32) keys and looked for bits 0 and 1. Below is a table of the probabilities of repeating bits 1 or 0 on a 256-bit key.
For example, the probability of a key having 16 ones or 16 zeros is 0.367964%
I can look up the code if you need to
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So this effectively means that bit lengths 15+ are unlikely to occur in a private key because they make up less than 1% of the sample population.