Re: Minimum Prime Gap?
- From: jankrihau@xxxxxxxxxxx
- Date: 3 Sep 2006 03:50:51 -0700
I wrote:
Gerry wrote:(...)
does anyone know the minimum values {a,b,c} of a quadratic function
f(x)=ax^2+bx+c
such that there is at least one prime between the values f(x) and
f(x+1).
I just tested {1/5,3/5,1/5} which seems to be good up to 9901.
I am tempted to require b = 0 (and then, that there should be a prime
for any non-negative integer value of x, which would imply that it also
holds for negative values).
Under this restriction the optimal choice seems to be a = 9/25, c = 2.
It is actually easy to verify that we can't use a smaller a simply by
considering the primes from 2 to 11 (which is obviously the only case
of 5 primes among 10 consecutive integers).
With f(x) = 9x^2 / 25 + 2, the interval [f(x), f(x + 1)] contains
exactly one prime for x = 0, 1, 2, 3, 4, 7, 9 and 28, and probably
more than one for all other x.
---
J K Haugland
http://home.no.net/zamunda
.
- Prev by Date: Re: algebra with finite field and isomorphic.
- Next by Date: Re: JSH: So I finally cheated
- Previous by thread: Re: Minimum Prime Gap?
- Next by thread: Re: Hahn-Banach, Order Unit question
- Index(es):
Relevant Pages
|
