Ask A Scientist Mathematics Archive

Author:      tim
What is the largest prime number?

Response #:  1 of 2
Author:      tee
There is no largest prime number (Euclid, et. al.).  Recently, (it seems
this statement will always be proper as computers keep getting faster)
another Mersenne prime has been discovered.  A look-up of this will connect
you to perfect numbers.  Many references exist.

Response #:  2 of 2
Author:      rcwinther
I heard about the new largest-known prime on the news, but I have not seen
anything about it in print, so I do not know how big it is.  The previous
record was the prime number 2^756839 - 1, a number of 227,832 digits.  Our
printer does about 5000 characters per page, so this works out to about 45
1/2 pages.  The new record-holder is likely to be significantly bigger.  A
questioner on the Computer Science BB says that the new record-holder is the
number 2^859433 - 1. This number would have 258,716 digits, requiring about
52 pages.