Linked Questions

5
votes
0answers
263 views

The inverse function of “Prime” [duplicate]

Consider p such that PrimeQ[p] == True. How do I compute n such that Prime[n] == p? In other words, what is the inverse ...
2
votes
0answers
132 views

What are the limits of the Prime-functions? [duplicate]

Will Prime and PrimePi test up to 3 * 10^12? Where can I find the limits for these funtions? ...
2
votes
0answers
72 views

Why can't I use OmegaPrime to find the Limit of Prime[n]? [duplicate]

I've looked at these links already; What are the limits of the Prime-functions? What is so special about Prime? which gave an answer for earlier versions of Mathematica. Yet when I try to input ...
2
votes
0answers
48 views

Internals of Prime function [duplicate]

Does anyone knows how exactly Prime works ? For example how Prime[1000000000] is calculated ? The only information I found was ...
21
votes
5answers
12k views

How to find the domain and range of a function with Mathematica?

I'm studying calculus and in some exercises I am asked to find the domain and range of a function. Does Mathematica have already a built-in function for this? I can imagine some ways of doing so, ...
13
votes
5answers
989 views

Double series over primes

I'm very curious if the following double series over primes has a closed form: $$\sum_{k \in \mathcal{P}}\sum_{n \in \mathcal{P}}\frac{1}{k\;n(k+n)^2}$$ where $\mathcal{P}$ denotes the set of all ...
8
votes
4answers
413 views

Generate PrimePower counting function

Is there a way to generate a counting function for prime powers - i.e. to create a similar function to PrimePi, but including prime powers. The following will, of ...
20
votes
2answers
3k views

Parallelization problem in LinearSolve and Minimize

My CPU has got 8 cores (it is Intel Core i7-2600 3.40 GHz). When I try to solve a linear matrix equation using LinearSolve for large matrices, Mathematica just uses 4 cores to solve the problem (CPU ...
15
votes
2answers
584 views

Why does iterating Prime in reverse order require much more time?

Say I would like to display the $10$ greatest primes that are less than $10^5$. I could do the following: ...
7
votes
2answers
795 views

Approximation to the prime counting function

Is there a function similar to PrimePi that gives approximate value for large numbers? In particular, I need a reasonably good approximation for $\pi(x)$, where $x\...
5
votes
3answers
490 views

Prime factor counting function

Is there any way I can speed up this prime factor counting function? (I am looking for all numbers in a range with 3 prime factors (counted with multiplicity).) ...
4
votes
1answer
788 views

How does Mathematica calculate the nth prime?

When I enter Prime[2000000000000], the two-trillionth prime, Mathematica gives 61427839512211 for the answer after several ...
2
votes
1answer
959 views

How to define a list that contains all primes less than x?

how can I define my own list in which I have all primes less than x?
1
vote
1answer
177 views

Interprocedural optimization

Lets say I want to build a list of the first 1000000 primes. This is simple enough, I can just do: AbsoluteTiming[plist = Table[Prime[i], {i, 1000000}];] and it ...
7
votes
0answers
143 views

Is this a reliable method for getting a list of very large primes?

As noted here, both PrimePi and Prime are documented as having their limits somwhere around $10^{15}.$ ...

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