SPECIAL NUMBERS

         SPECIAL NUMBERS

                       Smith number   

 666 is a Smith number    The sum of digits [6+6+6] is equal to the sum of the digits of the prime factors [2+3+3+(3+7)] 

The sum of seven Roman numerals is D+C+L+X+V+I=666. The letter M is missing. 
You also can write: DCLXVI=666.

            Gauss Sum  : The number 5050
There is a story about the famous mathematician Karl Friedrich Gauß (1777-1855), when he was a child. He should add the numbers 1 to 100. The teacher thought, that he would be busy with it for a long time. But Karl Friedrich found the sum 5050 after some minutes. Instead of adding the numbers one after the other, he made pairs of numbers and could multiply:

      1+2+3+4+...+50+51+...+97+98+99+100 
  = (1+100) + (2+99) + ... + (50+51)   = 50*101    = 5050.

Transcendental numbers:

                            pi = 3.1415 ...

                              e = 2.718 ...

Euler's constant, gamma 

= 0.577215 ... = lim n -> infinity > (1 + 1/2 + 1/3 + 1/4 + ... + 1/n - ln(n)) (Not proven to be transcendental, but generally believed to be by mathematicians.)

Catalan's constant, G = sum (-1)^k / (2k + 1 )^2 = 1 - 1/9 + 1/25 - 1/49 + ... (Not proven to be transcendental, but generally believed to be by mathematicians.)

Liouville's number

0.110001000000000000000001000 ... which has a one in the 1st, 2nd, 6th, 24th, etc. places and zeros elsewhere.

Chaitin's "constant"

The probability that a random algorithm halts. (Noam Elkies of Harvard notes that not only is this number transcendental but it is not computable.)

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