The World's Largest Prime

In November of 2003, Michael Shafer's computer discovered the 40th known Mersenne prime.

Short[2^20996011  -  1]

Short[2^20996011  -  1, 4]

Execute the below to see the full prime

2^20996011  -  1

kk  =  2^20996011  -  1;

This gives the number of times each digit appears, in decimal.  There are 6,320,430 digits.

Table[
      Count[IntegerDigits[2^20996011  -  1], n], {n, 0, 9}]

7 is the most common digit, 9 is the rarest.

Transpose[{Range[0, 9], {631705, 632720, 630989, 631467, 632004, 
          633283, 630929, 633503, 632964, 630866}}]

The original IBDWT algorithm for finding large Mersenne primes was developed in Mathematica by Richard Crandall.  At www.perfsci.com, the product "PrimeKit" is available, which is a precise, one-to-one collection of Notebooks for the algorithms in the Crandall/Pomerance "Prime numbers" book. The IBDWT algorithm is in there, as are all other book algorithms.  The Prime Numbers book is at http://library.wolfram.com/infocenter/Books/953/.