Look, they are all special. Every number is unique. As for the ones that people want to pay $100 for, I am not impressed. You can be illiterate and innumerate and see the pattern in 03030303 or 44444444. It's no big deal. We go ape over 04071776 and 07041776, but there's lots of dates. What dates are special to you? What I am looking for is numbers that are mathematical or physical constants. Pi 3.14159265 e 2.71828183 Avogadro's number 6.022140857(74)×1023 G gravitational constant 6.674 08 x 10-11 m3 kg-1 s-2 c 299 792 458 H Planck's constant 6.62607015 elementary charge 1.602176634 Fibonacci sequences 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 11235813 21345589 0112358 13213455 21345589 89144233 There's much more Sums Products Differences Quotients Powers Roots Products 09270243 9 x 27 = 243 62493038 62 x 49 = 3038 49623038 also of course and then the quotients 62/3038=49 and 49/3038=62 Squares 17530625 175 squared is 30625 30625175 would be the square root 57185193 57 cubed is 185193 And the cube root 18519357 My question is: Aside from looking at zillions of notes one at a time myself, how can I put this out to buy these notes from other collectors who look at numbers all the time? I would easily pay one dollar for a scan and maybe $10 for the note. Does that seem reasonable? I put it out here for comments.

All those esoteric serial numbers would not even register with 99% of people looking for fancy numbers - maybe you could seek out mathematicians who also collect currency - don't know where you will find a large group of mathematical numismatists or numismatic mathematicians, but good luck in your quest Here's a little pi humor, very little Write the expression for the volume of a thick crust pizza with height "a" and radius "z". Explanation: The formula for volume is π·(radius)2·(height). In this case, pi·z·z·a.

I'll definitely check my wallet, and see if I find those serial numbers. I've heard the pi serial number (A31415926A) was valuable. Other ones I did not know were valuable. You may find quite a few Fibonacci sequences sold on eBay as "incomplete ladders" or something like that.

Well, actually, would there not be 12 of them in every denomination? And would there not actually be potentially still others as Series 1935 and 1952 and 2003 and so on? In fact, the trailing letters go from A to Z, so like A31415926A, to L31415926Z, right? It is something I know little about.

A-A was just a generic example, but, yes, there would be more varieties of notes with issuing bank and block (suffix letter). Also, I’ve never seen a Z suffix, but I do have a Y suffix letter on a $1 note. I don’t think the Z suffix exists.

And then there is what I must call the the "Ramanujan-Erdős Numbers." In other words, as a conjecture, for every sequence of 8 integers, some interesting explanation exists. People who love numbers see these things all the time. The rest of us grind them out. I can look through all of my $1s here and see if I can crunch the serial numbers. (See my review of the biography of Paul Erdős, The Man Who Loved Only Numbers on my blog here.)

I have a math degree, but for some reason numbers on banknotes has never interested me. But your comment about any sequence of 8 integers having an interesting explanation reminds me of all those "find the next number" exercises where you're given something like: "If the first 4 numbers are: 5 22 76 124, what is the next number in the series?" I remember answering one in some class, as "777" or some such, with the explanation that the 5 numbers were the possible values of X in the equation: (x-5)*(x-22)*(x-76)*(x-124)*(x-777) = 0 This same mechanism could be used to convince yourself that *any* set of digits on a banknote were a mathematical equation, though I don't suggest collecting all of them

These days, that's correct: the FRB letter runs from A to L, and the block letter runs from A to Y (minus O, but plus *). So there are 12x25=300 possible blocks, though most series use well under half of them. In the old days, the alphabet included Z, and since the silver certificates and such didn't have FRB designations, they could use the full alphabet in both prefix and suffix positions. That allowed for 650 possible blocks, including stars, but fewer than 200 were actually used in practice. Back on topic: I think the demand (and hence the monetary value) for any particular serial number will depend mostly on how many people would recognize it as something special. So numbers like 00000001 and 12345678 will always be expensive, while something like your 17530625 example would probably sell for a few bucks tops. On the other hand, the more collectors are willing to pay for a certain item, the more dealers are willing to put effort into finding it for them. As a result, you could probably buy a dozen 00000001 notes this month if you had the money to pay for them, but good luck ever finding 17530625 for sale. Your examples of pi and e are likely somewhere in between. Someplace I've got a note that I saved from circulation because the first five digits were 31415xxx, so I can confirm that some folks actually look for pi. If the full 31415926 ever comes up for sale, I very much doubt that you'll get it for $10 or even $20...but for that very reason, it wouldn't surprise me if such a note actually came up for sale at some point. (Side note: The serial number I'd really like to find is 09699690, which is of interest to both currency collectors *and* math nerds....)

First 100 decimal places of Pi 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 So, just saying... 26433832 would be a "special" serial number In fact, with a sufficient scanning mechanism, it might be possible to being a set of notes that do present the numbers in Pi, given some length. You can find "Patterns in Pi" just as we go searching for "special" banknote numbers. https://necessaryfacts.blogspot.com/2012/11/patterns-in-pi.html For March 14, 2014, here in Austin, we had an aerial display writing the digits. https://necessaryfacts.blogspot.com/2014/03/pi-in-sky-over-austin.html