Questions on the number-theoretic functionality of Mathematica.

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7
votes
1answer
311 views

What is the confidence limit on this convergence?

When I run this, Product[n^MoebiusMu[n],{n,1,Infinity}] I get $\frac{1}{4 \pi^{2}}$ Over on Math Overflow they are saying it shouldn't happen. So, how do ...
7
votes
1answer
192 views

Testing for primality in quadratic rings?

Testing for primality in $\mathbb{Z}[\sqrt{-1}]$ in Mathematica is easy: PrimeQ[n, GaussianIntegers -> True] But how can I test for primality in, say, ...
5
votes
3answers
196 views

How could I implement the equivalent of NextPrime

I would like to know what an implementation of the function NextPrime would look like if it were implemented in Mathematica's core language.
6
votes
1answer
126 views

Implementing Remainder Tree

I want to implement Remainder Tree based on this. With the answers on SE I've come up with: ...
14
votes
2answers
413 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: ...
3
votes
0answers
248 views

Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
6
votes
1answer
445 views

Evaluate continued fraction

Mathematica has the ContinuedFraction[] function to give the continued fraction expansion of a rational (or approximation of a real) number. I'm interested in the ...
5
votes
0answers
100 views

Doing computations in a modulo ring

I need to perform some computations in a modulo ring, like Mod[Subfactorial[n], m] Mod[Binomial[n, k], m] However, this is obviously much too slow for large ...
10
votes
5answers
1k views

Fastest square number test

What is the fastest possible square number test in Mathematica 7, both for machine size and big integers? I presume in version 8 the fastest will be a dedicated C LibraryLink function.
21
votes
6answers
1k views

efficient way to count the number of zeros at the (right) end of a very large number

If I want to count the number of zeros at the (right) end of a large number, like $12345!$, I can use something like: Length[Last[Split[IntegerDigits[12345!]]]] ...
2
votes
0answers
119 views

PowersRepresentations Algorithm

I'm trying to understand the mathematics behind counting the number of representations of a positive integer by $n$ distinct $k$th powers, i.e. I would really like to know how to do the Mathematica ...
8
votes
0answers
462 views

Does Mathematica use the Elliptic Curve Method (ECM) in FactorInteger[]?

I'm not a mathematician, and I'm not even going to pretend that I understand anything of the ECM. But I know it can be a fast method for factorization. I benchmarked the factorization of ...
18
votes
4answers
684 views

Why does Mathematica claim there is no even prime?

I wonder if this is a bug, or if I'm misunderstanding something: Exists[n, EvenQ[n] && PrimeQ[n]] // Resolve (* ==> False *) So if I interpret this ...
23
votes
1answer
3k views

Finding long strings of identical digits in transcendental numbers

Introduction Describing the three main streams of present-day mathematical philosophy (formalism, Platonism and intuitionism) in a well-known book, The Emperor's New Mind, R. Penrose says: ...it ...