Determining If a Number is Prime
Date: 08/12/2004 at 21:24:52 From: Daryl Subject: Prime Numbers Is there a formula for finding if a number is prime? I've written a program that will tell you if a number is prime, but it is slow for larger numbers because it checks all numbers between 1 and the number to see if they are factors of the larger number. As you can see, checking a number in the billions would result in billions of divisions, which takes time. I've tried looking online, but haven't been able to find anything.
Date: 08/13/2004 at 12:21:49 From: Doctor Vogler Subject: Re: Prime Numbers Hi Daryl, Thanks for writing to Dr Math. There are several "formulas." They are called "primality tests." First there are the "pseudoprimality tests" which can quickly tell you if a number is NOT prime, but they can not guarantee that a number IS prime. The Fermat test is the best-known of these. The true primality tests are more complicated (which is why you usually start by checking if the number is clearly composite first, with a pseudoprimality test) but they can tell you conclusively whether a number is prime. In fact, a recent discovery was a "polynomial-time deterministic primality test" which means that it is "fast" by a particular technical definition of "fast." Other non-deterministic algorithms are more effective or more efficient, but this one is interesting theory. For precise descriptions of particular primality tests, search Google for "primality test." See also the account on MathWorld at Primality Test http://mathworld.wolfram.com/PrimalityTest.html If you have any questions about this or need more help, please write back and show me what you have been able to do, and I will try to offer further suggestions. - Doctor Vogler, The Math Forum http://mathforum.org/dr.math/
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