## Tuesday, February 15, 2011

### The mathematical constants e, pi

The Number e to 1 Million Digits

`2.7182818284590452353602874713526624977572470936999595749669676277240766303535...`

1 Million Digits of Pi

3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091

Find how many prime numbers appear in the first 100 digits of e and pi

For example, pi:
(1) : 3 ............. prime number
(2) : 31 ........... prime number
(3) : 314 .......... 314 = 2 * 157
(4) : 3141 ......... 3141 = 3^2 * 349
(5) : 31415 ........ 31415 = 5 * 61 * 103
(6) : 314159 ........ prime number
(7) : 3141592 ....... 3141592 = 2^3 * 392699

How many prime numbers can you find?

UPDATE: New puzzle

You are at a lake and have two empty containers capable of holding exactly
pi (=3.141592653589...) and e (= 2.7182818284590....) liters of liquid.

How many transfers of liquid will it take you to get a volume of liquid in one container that is within one percent of exactly one liter?