Find number property and write RPL program (HP-49G,G+, HP 50g)

[Gerson W. Barbosa]

(09-24-2014 12:53 PM)Dieter Wrote:  

(09-23-2014 05:41 PM)Gerson W. Barbosa Wrote:  This morning I opened my wallet and found only six bills therein (*). Oddly enough all their serial numbers are odd numbers.

Ah, between all those Brazilian Reals there also is a 100 Euro bill, issued by German Bundesbank.

Hello Dieter,

That one was was bought here at my bank early this year, part of 11 other 100-Euro bills (which were duely spent in Germany, by the way :-)
That particular serial number looked like a prime to me, and I decided to check it, upon which I discovered it was not only a prime number, but a special one. Not so special as a Mersenne primes, but special just the same -- and important in cryptography. As you can see, I didn't use any of my calculators to check for its primality as neither would have give this information ( this is a nice hint :-)

Quote:I do not know if this also applies to Brazilian currency, but the serial number of Euro bills follows a specific pattern. There is an initial letter (here X), followed by a ten-digit number and an 11th check digit. A valid serial number has certain properties, based on its modulo 9 value.

Does this point into the right direction or is it far off ?-)

I wasn't aware of the check digit, this is new to me, thanks! I mentioned somewhere in this trade those numbers are part of a subset of the set of primes, so the property is related itself to prime numbers. I also said the first three elements are { 2 3 5 }. OEIS gives too many sequences starting with these, so it won't help. But I also said 7 didn't belong in the list.
Only 22% of the first thousand prime numbers are in the list, and this percentage drops to about 8% for the first million numbers, so I was amazed at finding one 11-digit such prime in a universe of only 12 numbers.
Too many hints by now :-)

Once the property is found, the RPL program is almost straightforward on the HP-49G/G+ or 50g. I have two programs, one that gives the list of the first n elements and another that gives the list of the elements up to a certain value, sometimes with one element in excess ( 88.5 and 86 bytes, respectively).

Cheers,

Gerson.

P.S.: I traded the Euro bill back to Brazilian Reais yesterday ( I wouldn't keep it forever just because a mathematical property :-) and got 6 R$50 bills, one R$5 bill and one R$1 coin. Only two odd-number serials, none prime...