Do you think that one day someone will find a polynomial type formula that predicts the nth prime number? Or is there no pattern to them.
2007-10-04 19:43:08 · 3 answers · asked by Bender[OO] 3 in Science & Mathematics ➔ Mathematics
Actually, a few years ago, I read an article where a couple of mathematicians actually programmed a calculator to find such prime numbers..
..as to where or which article it was, I totally forgot, sorry.
Check out the link I found in wiki.
Hmm..you're asking for a prime-generating polynomial, eh?
When I read deeper, it seems those guys are still at it.
Yea, I guess you're right in saying that there's no polynomial that can generate primes for all x..yet.
2007-10-04 19:47:46 · answer #1 · answered by Hiro 3 · 1⤊ 0⤋
It has been proven that there can not exist a polynomial formula that gives all of the prime numbers.
It has also been proven that no polynomial formula can give only prime numbers. Some composite numbers will always appear.
Recursive prime number formulas have also been proven impossible. Given one prime, there is no simple way to find the next prime.
But it has been proven (by Euclid thousands of years ago) that there are an infinite number of primes.
Sorry for the bad news!
2007-10-04 20:50:43 · answer #2 · answered by Jeffrey K 7 · 0⤊ 0⤋
Hmm.. That's really interesting to think about. I don't think there is or ever will be a formula for that... but then again I'm no mathematician... so I'm most likely wrong.. But I do agree that we can program computers to find more prime numbers. I was reading a book about an autistic kid.. and the method he used was basically: list numbers, and then divide them by every integer possible. When nothing is left to divide by, you have a prime number. So that was pretty cool and I have no doubt that a computer would be able to do that.
2007-10-04 19:56:16 · answer #3 · answered by anebo129 1 · 0⤊ 0⤋