[QUOTE=Xyzzy;388025]We are so stupid.

:gah:

[CODE]_______________× [U][B]is[/B][/U] prime[/CODE]

We have emailed Ernst the request to verify our hints, just to make sure we have not made any other blunders.

We apologize for the error!

:max:[/QUOTE]

Assuming this was the only blunder on either of our parts, I've created a [URL="https://drive.google.com/file/d/0B72y7-pdB73beEN0WWRCTmhZUGM/view?usp=sharing"]new list with 691,157 numbers[/URL]. Just a hair fewer numbers than before. I'm guessing the sum of 43 is what accounts for nearly as many ending with 2 as 4, 6, and 8 combined.

So it ends in a 2?

[QUOTE=lavalamp;388036]So it ends in a 2?[/QUOTE]

Yep. This comes from:
[QUOTE=Xyzzy;387751]Let "E" represent an even digit and "O" represent an odd digit:

[CODE]EEEEEOOOEOEEOOOE[/CODE][/QUOTE]
And
[QUOTE=Xyzzy;388025][CODE]_______________× [U][B]is[/B][/U] prime[/CODE][/QUOTE]

Unless you happen to know of any other even one-digit primes.

I have some code running to trial factor 4, 6 and 8, but it hasn't come up with anything yet, we'll have to wait and see.

Ernst has verified that our hints thus far have been correct. (Not counting our mistake concerning the primality of 2!)

Our card number is in your new list.

Now will be the good time to cancel it. Pick up the phone, Mike...

:busted:

:omg:

[QUOTE=Xyzzy;388082]Ernst has verified that our hints thus far have been correct.[/QUOTE]

Oh, yeah - sorry, was meaning to post something to that effect but have been up for > 24 hours on an online Xmas shopping binge. (First hour was needed to enumerate from 0 - 999, though we were able to stop before having tried all 1000 combos.)

Did you really have to cancel the card? If so, couldn't you let us know what that last hint was that gave it away? Or am I missing the joke?

[QUOTE=Jayder;388110]Did you really have to cancel the card?[/QUOTE]Yes, it seemed like the appropriate thing to do. Fortunately our local bank can crank out a new card on the spot so it was only a minor inconvenience.

[QUOTE]If so, couldn't you let us know what that last hint was that gave it away?[/QUOTE]Our last (redacted) hint gave the sum of the first eight digits and the sum of the last eight digits.

:mike:

[QUOTE=Xyzzy;388138]Yes, it seemed like the appropriate thing to do. Fortunately our local bank can crank out a new card on the spot so it was only a minor inconvenience.

Our last (redacted) hint gave the sum of the first eight digits and the sum of the last eight digits.

:mike:[/QUOTE]
Here's the list of [(first eight sum, last eight sum), number of numbers with that pair]
[CODE][(21, 22), 123397]
[(23, 20), 106386]
[(25, 18), 93698]
[(19, 24), 91696]
[(27, 16), 83643]
[(17, 26), 54237]
[(29, 14), 41257]
[(15, 28), 39737]
[(31, 12), 21628]
[(13, 30), 16524]
[(33, 10), 10288]
[(11, 32), 5433]
[(35, 8), 2263]
[(9, 34), 800]
[(37, 6), 170][/CODE]
Unless I'm mistaken, the worst you could've done by your latest hint was to narrow it to 170 card numbers.

So much for the financial incentive!

That must have been an interesting conversation at the bank. "Hi, I need a new card with a new number for ... reasons. Hard to explain or understand reasons."

[QUOTE=lavalamp;388199]That must have been an interesting conversation at the bank. "Hi, I need a new card with a new number for ... reasons. Hard to explain or understand reasons."[/QUOTE]

"See, I gave out dozens of very precise hints on the Internet to random strangers, which seemed like a good idea at the time, and..."