385 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 ...
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153 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? ...
• 8,678
73 views

### How Prime[n] is implemented and why is that bounded? [duplicate]

How is Prime[n] implemented in Mathematica? I have just observed that calculating large primes is quite fast (but not in O(1) ...
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80 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 ...
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55 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 ...
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27 views

### Largest n in Prime[n] [duplicate]

What is the largest integer $n$ that the function Prime[n] can take?
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15k 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, ...
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1k 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 ...
• 1,415
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### Determining occurrence of a sequence of numbers in the first 50,000 primes

I have to determine how many of the first 50,000 prime numbers (digits) contain the sequence 5, 4, 3, in that order. The numbers don't have to necessarily be consecutive. For example, 566453 is a ...
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483 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 ...
• 8,678
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 ...
• 369
665 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: ...
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1k views

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