For anybody who wants to think about how such entry happened, it seems that the difference among the two presented numbers is in exactly 32 bytes (256 bits):
starting from the 162nd byte if I counted correctly, which means the first 5 * 32+1 (or 2 * 80+1) bytes are the same, then 32 bytes differ.
(The "easily factorable" number has two bytes which are represented as "bad1" in hex).
But thinking about the 256 bits, that's exactly the size of a block on which a typical symmetrical cypher can operate, which suggests some kind of a bug, although the offset of 161 byte is a bit strange.
The human would probably just change a few bits to achieve the same effect, not 256, unless he wanted to encode some message, and it doesn't look so. But see also the post of lawnchair_larry here.
The 161 bytes offset might be explained by corruption in an encoded version of the key. 161 bytes in binary data would be ~ 216 chars in base64. With an (unusual) line length of 72 the corruption would start exactly at the 4th line.
But: Mail clients should use 78 chars per text line, and GPG encodes base64 in lines of 64 chars length, so ignore my theory ;-).
Is there any sort of statistical analyses which could give some idea of whether those bits were generated randomly, by a human, or perhaps came from some other key?
They are just 256 bits. And if they come from a cypher they certainly can't be distinguished from the pure random bits or from the bits from any other key.
But if they come from some other key unmodified it would be possible to scan for the match, and it's a fast operation, as soon as we have the keys in which we'd like to search.
I was wondering about the possibility of distinguishing between a human opening a keyfile (I believe they are encoded in base64?) and manually overwriting pieces of it with random rubbish, or something else; humans make very poor RNGs, as anyone who has tried "randomly" mashing a keyboard will notice.
Please resist complaining about downvotes, as the site guidelines ask. Most unfairly downvoted comments get corrective upvotes after a while—that's what happened in the GP's case. Comments like this one, though, just add noise.
(The "easily factorable" number has two bytes which are represented as "bad1" in hex).
But thinking about the 256 bits, that's exactly the size of a block on which a typical symmetrical cypher can operate, which suggests some kind of a bug, although the offset of 161 byte is a bit strange.
The human would probably just change a few bits to achieve the same effect, not 256, unless he wanted to encode some message, and it doesn't look so. But see also the post of lawnchair_larry here.