For more information on how the largest prime number was found, see www.mersenne.org.
Python does support large numbers, but it's not very fast for such large numbers. There is a Python module called GMPY that uses the GMP (Gnu Multiple Precision) library for faster operations on large numbers. Both Python and GMP use a binary format to store large numbers. Binary format is most efficient for computation, but it is very slow to convert huge numbers from the internal binary format to a decimal format. I have written a library designed specifically to operate with huge numbers. It stores the numbers in a decimal format so conversion to decimal format is very fast. On my not-quite-ready-to-release development version, I can calculate, and convert to a string in decimal format, the largest known prime (2^25964951 - 1) in less than 10 seconds. My best time so far is 6.6 seconds. An early alpha-quality release is available at http://home.comcast.net/~casevh/ I also have release candidate versions of GMPY for Windows on that page. I'll try to get the next release and some demos up in a few days. Case -- http://mail.python.org/mailman/listinfo/python-list
