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3
votes
4answers
246 views

how to combine a list of the prime factors

For example, there is a list of prime factors. {{2, 1}, {3, 2}, {43, 5}, {26684839, 1}} How to combine them to the number ...
1
vote
2answers
232 views

How to generate a random, relatively prime number to p?

I'm sorry if this is an obvious question, but I'm a newbie and googling didn't help me much. Is there a way in Mathematica to generate a number q coprime with ...
1
vote
1answer
52 views

How to import a file for processing but not for displaying? [closed]

Here's my problem, I want to take what I have now for code ...
-1
votes
1answer
64 views
0
votes
2answers
78 views

Is there a manual way to generate a string of zeroes with a 2 at the end?

How do I get mathematica to display 33141015 zeroes and a 2 I've tried using 2*10^-33141016 but it just gives me scientific notation Is there a manual way to generate a string that looks like ...
3
votes
4answers
204 views

How to search for patterns to find the positions of prime numbers

I have a summation which yields a prime number at each location there is a 2, and I do not know how to search for the 2's. ...
14
votes
3answers
595 views

How can FactorInteger be so slow if PrimeQ is fast?

My 8th grade son had a homework problem to find a prime factor of $99!-1$. I thought to be clever/lazy and used FactorInteger[99!-1], but it takes forever. ...
1
vote
2answers
77 views

Infinite sums with Boole and EvenQ

Suppose I am interested in a sum across a set of even numbers, such as: Sum[x, {x, 2, 20, 2}] 110 or ...
3
votes
2answers
135 views

Prime power list

Update Is there any better way of generating the nth prime power? Chip Hurst gave a great solution for a list below, so ...
0
votes
1answer
59 views

Consecutive integers that can be written as the product of three distinct primes

Mathematica novice here. I want to start with a list of integers that are the product of three distinct primes m,n, and o, where 2 <= m|n|o < 2000. ...
2
votes
1answer
84 views

One of the factors greater than $x$ [closed]

Is there an easy way to tell Mathematica to find one of the prime factors of $n$ greater than $x$. For example, if $n=1299709\cdot 7919 \cdot 17$, is there a way to request a factor greater than ...
-2
votes
1answer
101 views

Missing Primes in List [closed]

In the following code why do I get even numbers instead of primes only: ...
4
votes
2answers
257 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 ...
11
votes
4answers
520 views

Set of integers not divisible by smaller set of primes

Let $p_n$ be the sequence of prime numbers, and $s(x,n)=$ the set of integers less or equal than $x$ that are not divisible by $p_1,\dots,p_n.$ I can define it as follows: ...
0
votes
2answers
122 views

prime-palindromic number selected from a list

I want to find all prime-palindromic numbers up to 5000. Prime-palindromic numbers are numbers that themselves and their reverse digits are both primes. For example, 31 is a prime-palindromic number ...
8
votes
5answers
959 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 ...
2
votes
1answer
103 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 $$ \{\{2\}\},$$$$ ...
5
votes
0answers
120 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 ...
2
votes
0answers
112 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 ...
4
votes
2answers
155 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 ...
14
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). ...
3
votes
1answer
176 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
3answers
145 views

Finding primes that have certain property

Let S[p] denote the sum of digits of p. A prime p is said to be stubborn if none of ...
0
votes
0answers
43 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 ...
1
vote
0answers
36 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 ...
6
votes
2answers
331 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. ...
1
vote
1answer
226 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). ...
8
votes
4answers
330 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 ...
0
votes
0answers
279 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 ...
2
votes
0answers
115 views

Double sum over primes [duplicate]

Can anyone tell me the value of the sum $$\sum_{p\in \mathcal{P}}\sum_{n=1}^{\infty}\frac{\log (p^n)}{2}\left[\,p^{-n}-\psi\left(\frac{p^n+2}{2}\right)+\psi\left(\frac{p^n+1}{2}\right)\right].$$ ...
12
votes
5answers
668 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 ...
11
votes
5answers
1k 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? ...
12
votes
3answers
496 views

Next highly composite number?

R language has this function 'nextn' (link) which computes the next highly composite number greater than a given one, which is used to find the optimal padding size for the subsequent FFT operation. ...
4
votes
1answer
401 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 ...
8
votes
3answers
549 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: ...
14
votes
2answers
451 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: ...
13
votes
2answers
416 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 ...
5
votes
1answer
435 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 ...
8
votes
1answer
205 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, ...
1
vote
1answer
457 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 ...
34
votes
9answers
2k 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 ...
39
votes
2answers
4k views

What is so special about Prime?

When we try to evaluate Prime on big numbers (e.g. 10^13) we encounter the following issue : ...
21
votes
4answers
809 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 ...