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### Prime Number 2001, Sieve of Eratosthenes

Date: 01/25/97 at 16:51:07
From: Davenports
Subject: 2001

Dear Dr. Math,

Is 2001 a prime number?

Thanks-
J and G

Date: 01/25/97 at 17:47:27
From: Doctor Wallace
Subject: Re: 2001

Hi J and G,

What an interesting question you have there!  Since you didn't say,
I have no idea in what context this question comes up.  Maybe you
are just curious?

Well, you might be interested to know that there is a branch of
mathematics called number theory that deals with questions like this
one.  Further, within number theory there is a mini branch of math
called, you guessed it, prime number theory!  Most of its methods for
determining if a number is or isn't prime are not magical, just very,
very time consuming and "number crunching."  They are usually carried
out by powerful, expensive computers.

The oldest I know of is called the Sieve of Eratosthenes. His method
gives all the prime numbers less than any given integer n, by deleting
from the set of all integers less than n the multiples of each of the
primes up to the square root of n. For example, to find out whether
1987 is prime, you only need to check that it is not divisible by 3,
5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43.  We can stop there,
since the square root of 1987 is 44.57.  We only need to check primes
because every integer can be factored into a unique product of primes.
This is called its "prime factorization."

So what am I really suggesting to you?  You have to go trial and error
number crunching.  But Eratosthenes says you only have to check the
primes up to the square root of your number.  So for 2001, you may
also stop with 43, because the square root of 2001 is 44.73.

So, have you tried all these primes to see if they go into 2001?  If
you do it for 1987, you'll find out that 1987 is prime.  But is 2001?

Thanks for writing.  I hope this helps.  If you need more help, don't
hesitate to write again!

-Doctor Wallace,  The Math Forum
Check out our web site!

Associated Topics:
High School Number Theory
Middle School Prime Numbers

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