- Now that I think about it better, I see that I was fooled by your proposal!

:D

What we want is not a polynomial whose _roots_ are primes, what we want is

a polynomial which generates as much primes as possible with its _image_.

I.e., what we want is to maximize p such that the sequence p({1,2,3,...})

gives the biggest possible "prime head".

The classical example of Euler, p(x)=x^2-x+41, e.g., gives p(1)=41,

p(2)=43, p(3)=47, and so on.

Regards,

Jose Brox

2013/7/26 Jose Ramón Brox <ambroxius@...>

>

--

>

>

> 2013/7/26 djbroadhurst <d.broadhurst@...>

>

>> **

>> This polynomial performs better:

>>

>> polinterpolate(vector(100,k,prime(k)))

>>

>>

> Sure! But it (I suppose) does not satisfy the implicit assumption

> (explicit in the contest) that the primes must be consecutive.

>

> Regards,

> Jose

>

>

La verdad (blog de raciocinio político e información

social)<http://josebrox.blogspot.com/>

[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com,

"WarrenS" <warren.wds@...> wrote:

> > Let N(a,n1,n2) be the number of primes of the form

Bad models.

> > n^2+n+a with n in [n1,n1+n2]. Then the data

> >

> > N(247757,0,10^6) = 324001

> > N(3399714628553118047,0,10^6) = 251841

> >

> > seem to favour the smaller value of a. Yet these data

> >

> > N(247757,10^12,10^6) = 148817

> > N(3399714628553118047,10^12,10^6) = 193947

> >

> > indicate that the larger value of a is better, in the long run.

>

> --these numbers seem to be in vast violation of naive statistical

> models.

> Is the reason, that the length n2 of the sampling interval,

No. Rather it is that n1, the begining of the sampling

> needs to be substantially larger than a, in order for naive

> statistical models to become reasonably valid?

interval, needs to be substantially larger than sqrt(a),

for the HL heuristic to win out. Clearly when

n1 < sqrt(3399714628553118047), Marion was comparing apples

and oranges, since log(n^2+n+a) was dominated by "a".

All I did was to level the playing field, here:

> N(247757,10^12,10^6) = 148817

to allow the HL heuristic to show through.

> N(3399714628553118047,10^12,10^6) = 193947

It's a simple as that. No shock-horror for statisticians;

Just a trivial observation by a log-lover :-)

David