Questions on testing and computing prime numbers.

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1
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1answer
44 views

Timing and ListPlot

I am currently trying to examine the Timing function as it relates to generating primes and factorize large integers. What I want to do is to visualize how time ...
3
votes
1answer
49 views

A function about prime gaps

I want to define a $f$ function on Mathematica such as this. $f[k]$ gives the smallest $m$ holds $2k=Prime[m+1]-Prime[m]$. For example, $$f[1]=2$$ $$f[2]=4$$ $$f[3]=9$$ $$f[4]=24$$ How can i do ...
4
votes
2answers
61 views

Goldbach Partition

I want to check the Goldbach conjecture for big number of $n$, but I don't know how to define this in Mathematica. There are my questions: Find a pair of primes $(p,q)$ for every even integer $n$, ...
8
votes
5answers
311 views

Finding large primes

I'm quite new to Mathematica and I am trying to find large prime numbers that can be written using only the digits 0, 1, 2 and 3 and more than half of these digits have to be 0. For example 1000 and ...
1
vote
1answer
178 views

Why can't mathematica tell me the smallest prime number?

I entered MinValue[{Prime[n], n>=1 && Element[n, Integers]}, n] But I just got back what I entered. Why can mathematica not tell me the smallest ...
1
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5answers
357 views

Prime factorization

I am trying to find a code that will output the prime factor decomposition of a number but for some reason I keep getting error messages. It is supposed to output the exponent of 2 and the odd factor. ...
4
votes
1answer
65 views

Create a function for $\Pi^{-1}(n)$

Is it possible to create a function that gives the inverse of pP[x_] := Sum[PrimePi[x^(1/k)]/k, {k, 1, Floor[Log2[x]]}] i.e., a function that plots ...
1
vote
0answers
58 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 ...
7
votes
0answers
125 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 $10^{15}.$ ...
9
votes
1answer
176 views

Finding large prime gaps

I am using basic searches for prime gaps as follows: ...
1
vote
1answer
186 views

Something wrong with FromDigits?

NestList[RotateLeft, IntegerDigits[19], 1] FromDigits[%] (* WRONG *) ...
0
votes
1answer
191 views

Prime number The Ulam spiral [closed]

I want a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. I was able to display the ...
3
votes
4answers
276 views

Permuted Prime Numbers

How can I produce all 3-digit and 4-digit prime numbers [100-9999] in which, all permutations of all digits produce again a prime number, such as 311, 131, 113, ...
0
votes
1answer
95 views

A question about calculus and Programming

I am a very new user and I would like to know how to calculate the following operations in Mathematica. Honestly this is not a homework. I am an french architect and I would like to be back in Math ...
3
votes
4answers
298 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
347 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
64 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
157 views
0
votes
2answers
89 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
282 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
687 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
100 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
216 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
75 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
103 views

One of the factors greater than $x$

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 ...
4
votes
2answers
343 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
554 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
194 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 ...
14
votes
6answers
1k 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 ...
3
votes
2answers
132 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 $$ \{\{2\}\},$$$$ ...
10
votes
1answer
201 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
134 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 ...
5
votes
2answers
183 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 ...
15
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
205 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
159 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
44 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
38 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
351 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
292 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
353 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 ...
2
votes
0answers
119 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
767 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 ...
12
votes
5answers
2k 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? ...
13
votes
3answers
562 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
487 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 ...
5
votes
3answers
285 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.
9
votes
3answers
593 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: ...
15
votes
2answers
482 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
441 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 ...