RFI… Can Any Number Theorist (or others) Reply to This?

I can’t answer the following for one of my readers, but maybe someone else can (about a Fermat factoring variant)???

Well over 3 years ago I posted this little gem from Futility Closet:

"In 1643, Marin Mersenne wrote to Pierre de Fermat asking whether 100895598169 were a prime number.

Fermat replied immediately that it's the product of 898423 and 112303, both of which are prime.

To this day, no one knows how he knew this. Has a powerful factoring technique been lost?"

At the time, one comment came in (from someone named Walt), as follows:

“It is not that surprising if we assume that Fermat used what we call Fermat's factoring method. Upon multiplying by the cofactor of 8 (and using difference of pronic numbers instead of squares since the number is now even) he would find this pair of factors on the first try. (I am assuming that taking the square root of a 12-digit number was feasible. Also, I have no idea how difficult it was at that time for him to prove the primality of the resulting 6-digit factors.)
In fact, 8 * 112303 = 898424 = 1 + 898423. This is a remarkable coincidence and makes me wonder if Mersenne used this relation to construct the problem in the first place.”

Now (3+ years later) I’ve received an inquiry from a retired German mathematician, who recently ran across the post & comment, and asking in part about the:

“…. variant of ‘what we call Fermat's factoring method. Upon multiplying by the cofactor of 8 (and using difference of pronic numbers instead of squares since the number is now even) …’  I am wondering about (t)his remark to use differences of pronic numbers: I have never heard of that variant or read about it in any book. He [Walt] does not quote any references, so he seems to consider this variant as being well known. In fact, it is not too difficult to figure out the formula a*(a+1) - b*(b+1) = (a+b+1)*(a-b) that turns such a difference into a product, and to check that one may thus devise a factorization method for even numbers. I am wondering if this has been published anywhere.”

Can anyone provide an answer???