Re: Percentage of Prime Numbers

On May 11, 9:58 am, Jeremy Boden <jer...@xxxxxxxxxxxxxxx> wrote:
On Sun, 11 May 2008 08:17:23 -0400, T.H. Ray wrote:
Hi,

I just checked my 10-€-Banknote and found out the serial number is a
prime number. I just asked the European Central Bank how many
Banknotes circulate and want now to find out the chance that a
randomly picked banknote has a prime serial number. So - is there any
possibility (without crashing my PC) to find out how many prime
numbers are in a given area of numbers?

Thanks a lot!

An intriguing and interesting question.  The prime number theorem,
described here:

http://en.wikipedia.org/wiki/Prime_number_theorem

will tell you the percentage of primes below a given number.  I have no
idea, however, how the Central Bank assigns serial numbers.

Almost certainly one or two digits will be check digits - makes printing
your own notes substantially harder.

So the number might not be prime without the check
digits.

And do the serial numbers start at 0?

Do any serial numbers have leading 0's?

That can affect the probability.



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