There are computationally inefficient formulas:

Define a function F(a,b) to be equal to a/gcd(a,b^10).

Next_prime(x) is then equal to:

sum for n=x to Infinity of floor(1/F(n!,x!))

I believe this function is correct for all integers x >= 0.

In practice, you only need to sum until you get a zero value,

and all subsequent values will be zero.

What makes the above computationally infeasible, even for relatively

small numbers, is that x! is already beyond representation in any

known computer long before finding primes becomes difficult.

On 4/2/2013 12:43 PM, whygee@... wrote:

> Le 2013-04-02 21:34, viva8698 a écrit :

>> Recently we had a great discussion during a meeting with colleague

>> matematicians and we opened a theme that seems to get quite an

>> interesting intellectual quiz:

>>

>> What would be the consequences if Mr. X would have a formula to

>> calculate from a given prime the whole ordered series of the

>> subsequent primes one after the other?

>

> There is no such computationally efficient *formula*.

>

> However there are _algorithms_, with obvious drawbacks.

> It's not what most mathematicians want, hope or dream of,

> but Mathematics is not created to please us either.

>

>

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