From a posting to the Math Fun mailing list by R. W. Gosper, Dec 03 2009:

(Begin)
Gosper: I just reordered checks.
Bank Lady: Where would you like the numbering to start?
Gosper: What was my last one?
Bank Lady: 1093
Gosper: Well then obviously 3511 .
Bank Lady: [Opens mouth. Decides not to ask. Resumes typing.]
(End)


My question : How many checks can you order for Mr. Gosper's checkbook, using his numbering system?

(In reply to Solution by Chris, PhD)

It seems clear that is the sought connection between the numbers, but it just doesn't seem to fit.

You can't just order a single check.  You can make then start at any number up to 5 digits but you still have to buy a minimum of 1 box which is like 125 checks.

It also makes you wonder how he ran out of checks at 1093 and not an even 1100 or 1125. 

So it would seem you still order over 7500 checks leaving a pretty much arbitrary gap between these two primes.

I'll also point out that these Wieferich Primes may not be the only ones.  It has been conjectured that there are infinitely many.

Posted by Jer on 2012-09-20 22:34:50