That formula should read:

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

On 4/2/2013 4:54 PM, Jack Brennen wrote:

> 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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