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Prime Number Generation
Name: Peter
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: 7/9/2005
Question:
How can we generate a prime number?
Replies:
Prime numbers have intrigued mathematicians for centuries. It is an
important sub-branch of mathematics called "number theory". Despite the
efforts of the best mathematical minds over the centuries, there is no
general "formula" for generating prime numbers. There are some
approximations, and there are theorems predicting the number of prime
numbers less than a particular upper bound. As of 2003 the largest known
prime number is:
The 39th Mersenne prime
m39 = 213,466,917-1
is the largest known prime number (as of the time of this writing, May 23,
2003). In the decimal system it requires 4,053,946 digits to be written
fully. Most of this page is taken up by those digits. You can appreciate the
size of this number, and perhaps have a psychedelic experience, by scrolling
this page across your screen. If you find that the last digit is even then
this file was accidentally truncated in the process of downloading it! You
can find it written out on the web site:
http://www.math.utah.edu/~alfeld/math/largeprime.html
By the way Mersenne primes are prime numbers of the form: Mp = (2^n) - 1.
This formula generates prime numbers but also misses some. To investigate
prime numbers further, you can start with the sites:
http://mathworld.wolfram.com/PrimeFactor.html
http://www.utm.edu/research/primes/notes/conjectures/
There are many interesting relations involving prime numbers which have been
examined by computer and are apparently true, but for which no mathematical
proof is known. These are known as "conjectures". What is so interesting
about primes is that they do not involve complicated numbers -- just the
"counting numbers" 1, 2, 3, ... yet they hold many mysteries.
Vince Calder
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Update: June 2012
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