## 24978Re: [PrimeNumbers] What if Mr. X would have a formula for the prime series?

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• Apr 2, 2013
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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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>>
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>>
>
>
>
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