I am aware of huge work having been done on prime numbers to see if their occurence in the series 1,2,3,5,7,11,13,17.........'n' can actually be predicted. I am aware of the 'Sieve of Eratosthenes' and of work done by Euler and others. But I wish to know if there are still people out there who believe such an equation (to predict prime numbers based on previous primes) is believed in or is the product of any ongoing study. The implications for discovery in this area are surely enormous.
2006-09-17 00:29:52 · 6 answers · asked by democracynow 2 in Science & Mathematics ➔ Mathematics
Given the importance of prime numbers in cryptology, there is a lot of research in devising methods for identifying prime numbers. There are probably as many mathematicians searching for such a method as there are mathematicians looking for a proof that such a method cannot exist.
So, anyone who believes there is a predicting equation out there, yet to be discovered, are in good company. Those who believe otherwise are in equally good company.
We may never know...
2006-09-17 00:44:39 · answer #1 · answered by Vincent G 7 · 0⤊ 0⤋
An expression in 26 variables was discovered by Matijasevich in 1976. If you assign any integer values at all to his 26 variables, it evaluates either to a negative number, or a positive prime number. Mathematicians seem to be agreed that this is interesting, but useless.
If you know enough values of the zeroes of the Riemann Zeta function (no, don't ask, I don't know either), you can plug them into a prime-counting formula that is so accurate that it will give you a constant value as you step across a composite number, and an increment by one as you step across a prime number. However, it seems to be more work to get enough of these zeroes accurately enough (lots and lots, and very very very accurately) to make this any better than just testing the number you were thinking of stepping across.
Generating primes for Internet security, based on RSA and similar encryption, is easy enough in practice. The security is perfectly safe no matter how easy it becomes to generate primes in the future, because it lies in the difficulty of factoring the PRODUCT of two large primes, and that is fundamentally so difficult that being able to generate primes at lightning speed would not make it any easier.
2006-09-17 03:09:45 · answer #2 · answered by Anonymous · 0⤊ 0⤋
a million isn't a best variety best variety - Which variety might want to be divided by employing itself except a million. eg. 2,3,5,7,eleven,13,17 2/2 = a million 3/3 = a million 7/7 = a million eleven/eleven = a million 13/13 = a million 17/17 = a million 12 isn't a best variety because 12/2 = 6 (not a million) 12/3 = 4 (not a million) 12/4 = 3 (not a million) so on.
2016-11-27 19:58:08 · answer #3 · answered by ? 4 · 0⤊ 0⤋
If we let pi(n) denote the number of primes less than n and Li(x) denote the logarithmic integral, li(x)=\int_{0}^{x} 1/(ln(t) dt, the Prime Number theorem states that pi(n) approx li(n).
2006-09-17 01:03:58 · answer #4 · answered by Anonymous · 0⤊ 0⤋
One does not predict prime numbers. They just are! you just have to find them. DO THE MATH.
2006-09-17 00:40:08 · answer #5 · answered by Bob S 3 · 0⤊ 1⤋
Oh yes, the implications are HUGE!!! Huh????? E=MC2 does it for me every time!
2006-09-17 00:34:38 · answer #6 · answered by Fluffy 5 · 0⤊ 1⤋