Charles Babbage's Conjecture/Historical Note

Historical Note on Charles Babbage's Conjecture
The name Charles Babbage's Conjecture has been coined by as a convenient label to apply to a statement whose full description is unwieldy.

Note that the name Babbage's Conjecture is already used in the literature to refer to a conjecture suggested by.

According to 's $1997$ work, the refutation is the work of , who also determined that no other such counterexample exists for any $n$ less than $150 \, 000$.

However, this still needs to be corroborated by evidence on the internet.

also suggests that any higher power of $16 \, 843$ is also a counterexample, which would be interesting, as it would suggest that, for example:
 * $16 \, 843^4 \mathrel \backslash \dbinom {2 \times 16 \, 843^2 - 1} {16 \, 843^2 - 1} - 1$

It appears prudent, therefore, to ascertain whether is actually correct in his citation of $16 \, 843$ being the counterexample that  actually discovered.

Hence research is invited into the literature, to find the original work and to confirm what is claimed here.