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32
votes
9answers
1k views

Happy 2K prime question

This being the Q number 2K in the site, and this being the day we got the confirmation of mathematica.se graduating soon, I think a celebration question is in order. So... What is the fastest way to ...
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: ...
12
votes
2answers
351 views

Is there a way to use functions like Prime[n] within Solve[]?

I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use Solve[ Prime[n] + Prime[m] == 100, {n, m}] But that ...
10
votes
4answers
2k views

Semi prime numbers

The high school textbook I am using has the example of semi-prime numbers. They wanted students to find (by "perspiration") all the semi-prime numbers less than $50$ (for a question on set theory). ...
10
votes
5answers
643 views

How can I simulate this animation of checking for prime numbers?

I can only implement a very simple one, I want to make my code look like that. Any better ideas? ...
10
votes
5answers
489 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
3answers
487 views

Fast Sieve Implementation

I'm going to write a code to compete in performance with NewPGen. The goal is to sieve numbers that have small factors. Mine is very slow in compare with NewPGen. Here's my code: ...
7
votes
4answers
276 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 ...
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, ...
6
votes
4answers
353 views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
6
votes
2answers
302 views

Memory management and speed for Fast GCD

Let's say that we have some $300\,\text{K}$ digits (arbitrary function) and want to trial factor with $100{,}000{,}000$ first prime numbers. ...
5
votes
1answer
348 views

Time approximation of decrypting RSA algorithm

I've written a function that encrypts a text using the RSA algorithm. It then decrypts it using prime factorization, and takes the time it took to decrypt it and puts it in a vector together with the ...
5
votes
0answers
93 views

Is there a PrimeQ whose accuracy guarantee you can adjust?

Say I have a list of a million integers each with a million digits, and I want a crude sieve to see which have a chance at being prime. Mathematica has a PrimeQ function, which appears to be slow ...
3
votes
1answer
272 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 ...
3
votes
1answer
157 views

Faster Solve for Fermat 4n+1 conjecture

Assuming that Fermat 4n+1 conjecture (each prime of the form 4n+1 is the sum of two squares) is true then I like to solve the ...
2
votes
2answers
126 views

FactorInteger over UFDs

How can I factor 'integers' over other quadratic number fields (not just gaussian integers). For instance, how could I factor $7 = (3 + ω)(2 − ω)$ over Eisenstein integers ($ω = \frac{-1+ I ...
2
votes
0answers
95 views

Displaying primes as a 3D array of spheres

I am currently learning my way through Mathematica and have stumbled upon a strange problem. It is asking me to implement PrimeQ into ...
2
votes
0answers
110 views

Double sum over primes [duplicate]

Can anyone tell me the value of the sum $$\sum_{p\in \mathcal{P}}\sum_{n=1}^{\infty}\frac{\log (p^n)}{2}\left[\,p^{-n}-\psi\left(\frac{p^n+2}{2}\right)+\psi\left(\frac{p^n+1}{2}\right)\right].$$ ...
1
vote
1answer
416 views

Equivalent of Python's “all” function in Mathematica

The Python function def isPrime(n): return all(n % i for i in xrange(2, n)) checks if a number is a prime number by using ...
1
vote
1answer
82 views

Symbolic multiplicative partitions

Let $p_n\#\equiv\prod_{k=1}^{n}p_k$ (primorial): p[n_] := Times @@ Prime[Range[n]] then the multiplicative partitions of $p_{1,2,3,4}\#$ are $$ \{\{2\}\},$$$$ ...
1
vote
1answer
163 views

How to represent very long integers with at-most-8-digit(base-10) short integers with * and +

I need an algorithm in Mathematica, which can represent any very long integer, prime or not, into the the product operation "*" and sum "+" forms by short integers (not more than 8 decimal digits). ...
1
vote
0answers
30 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 ...
0
votes
0answers
42 views

Limits of PrimeNu [duplicate]

Is there any way to find distinct prime factors for very large numbers using Prime and/or PrimePi that exceeds the ...
0
votes
0answers
195 views

Hurwitz-Lerch transcendent

I want to compute the following sum over primes: $$\sum\limits_{p \text{ prime}}\sum\limits_{k=1}^\infty(\log(p^k))\left(\frac{1}{2p^k} - \Phi[-1,1,p^k]\right),$$ where $\Phi[z,s,a]$ is the ...
-1
votes
2answers
147 views

How to print prime numbers [closed]

I want to know how can I print out a list of prime numbers. Should I use For, Do, If, ...