Tuesday, March 15, 2005
This Day:

A prime number is an integer (> 1) that is divisible by 1 and itself (for example, 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on). Mathematicians have tried in vain to find any order in the distribution of the prime numbers, and the prime sequence remains the most interesting sequence of numbers. Prime numbers can be computed easily (for example, by using the Sieve of Eratosthenes). There are an infinite number of prime numbers, and it is always an interesting project to find the largest known prime. An interesting subset of the prime numbers is the set of the so-called Mersenne Primes, named after the 17th century Frenchman, Marin Mersenne.

Marin Mersenne (1588-1648)
Mersenne primes are of the form Mp = 2p-1, where p is also prime. The first eight such primes are 3, 7, 31, 127, 8191, 131071, 524287, and 2147483647. Last month, using the Great Internet Mersenne Prime Search (GIMPS), Dr. Martin Nowak discovered the largest known prime, which is also a Mersenne prime. The prime number is 225,964,951-1, and has 7,816,230 digits (Click here for the full number!). It took more than 50 days of calculations on Dr. Nowak's 2.4 GHz Pentium 4 computer. The discovery is the eighth record prime for the GIMPS project.
As computing power increases, more and more such primes will be found :-).

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3/15/2005   5 comments Post a Comment

5 Comments:

At March 16, 2005 4:26 AM, Blogger Wayne Smallman said...
Didn't some young school girl from over here (Britain) come up with an encryption algorithm using prime numbers?

Can't remember how it works now, but it was something along the lines of taking a large random prime number and multiplying it and then dividing it, which rendered the number impenetrable.

Anyway, question: what (if any?) is the practical use of a proof for a pattern to prime number calculation?
 
At March 16, 2005 7:05 AM, Blogger LEMNA said...
Emmm,Thanks alot pal,it was nice description,we has these in school,I remembered those years with your post:)Now I wanna know its usage in other sciences?As your friend has written its practical usage?
 
At March 16, 2005 8:20 AM, Blogger Sray said...
Large prime numbers have applications in encryption, for example, in the public-key encryption (Pretty-Good-Privacy, or PGP algorithm). Since prime numbers do not follow any pattern (if it exists, it hasnt been found yet), such PGP algorithms are virtually unbreakable if sufficiently large primes (128bit, 256bit) are used.

Applications of a prime pattern:
a) Code-breaking! If a pattern is found, it will be easy to break all codes, and there will be chaos!
b) There might be connections between the prime series, and physics (the precise ratios of different constants like grav-constant G, speed-of-light c, etc. might depend upon some property of the prime series). It is a very intriguing prospect, which would prove that there is one and only one way of constructing a universe, since properties of prime numbers are independent of which universe we live in.
c) Primes possibly follow a fractal pattern.. this might have applications in understanding deep problems in chaos/turbulence theory.
d) Just for fun!! Who cares about applications? Primes are interesting numbers in their own right :-).
 
At March 16, 2005 8:49 AM, Blogger Wayne Smallman said...
The love of numbers is somewhat lost on me.

I have a deep indifference towards mathematics .. chiefly because I'm crap at it.

That's not to say I don't appreciate the elegance and the interest for people like yourself.

I take consolation in some research conducted recently that showed some people -- no matter how hard they might try -- will never be able to grasp mathematics with anything more than a mediocre understanding.

Hey! That's me!
 
At March 16, 2005 9:13 AM, Blogger Sray said...
Not everyone is good in everything! You are good in things you do, and I hope I am in things I do. What is important is you keep a healthy thirst for knowledge, and keep your mind open to new possibilities :-).
 

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