Questions on testing and computing prime numbers.

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0
votes
0answers
35 views

Prime-Generating Cellular Automaton

I'm trying to use these ...
1
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1answer
68 views

Generating a very large list of integers not divisible by a set of primes

I have read (58520), but the solutions there do not work when using a large maximum value because they rely on Range. For example, ...
3
votes
3answers
175 views

OEIS A144311 Generating function

I'm looking for a way to use calculate OEIS A144311 efficiently in Mathematica. First, let's define the series. In one sense or another, this series considers the number between "relative" twin ...
8
votes
1answer
129 views

Accuracy of PrimeQ function

Using PrimeQ in Mathematica 10 on integers up to $2\cdot 10^{5717}$ the function appears to work. The Documentation for Mathematica 5 says that ...
2
votes
1answer
65 views

Twin Prime Max Gaps (Performance Tuning)

Ok, let's build a foundation here: A common way of testing primality, is dividing by all primes smaller than the number's square root. For instance, $97$ is prime because dividing by none of the ...
-1
votes
1answer
51 views

Generate list of first 100 prime number? [closed]

I know how to generate a list of prime numbers up to a limit, but how would I generate the first 100 prime numbers in a list?
2
votes
2answers
172 views

Brute force evidence of possible proof of twin prime conjecture

Trying to avoid shelling out hundreds of dollars so I'm using what I can for free online. This is what I've come up with so far: https://dl.dropboxusercontent.com/u/76769933/TwinPrimes%203Podd.cdf ...
3
votes
1answer
20 views

What is the form of a PrimalityProving`PrimeQCertificate?

I understand the format of a proof of compositeness of an integer produced by PrimeQCertificate: it's well-documented that ...
3
votes
1answer
96 views

Plot prime numbers in spiral form, in the clockwise direction

I want to plot first 100 Prime numbers in circular format (on circular orbit) in Mathematica. How can i do this?
5
votes
0answers
62 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 ...
10
votes
2answers
231 views

Primes Race (Mathematica Efficiency)

I am currently working with a paper that deals with this concept of Prime Races. You essentially create a large list of prime numbers and then split that list into two teams. You are assigned to ...
3
votes
1answer
117 views

Memory limit hit: optimize code for finding twin primes

I need some help optimizing a Mathematica code so that it'll not max out RAM. Here's the code: Cell 1 ...
1
vote
1answer
53 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 ...
0
votes
0answers
61 views

Riemann Zeta function definition was expanded by Euler with an infinite product series [duplicate]

The Euler infinite product series definition for Riemann's zeta function requires that Mathematica use all prime numbers in the product series. Can anyone help me with the code that will give a ...
3
votes
1answer
50 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 that?...
4
votes
2answers
103 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 $n$, ...
9
votes
5answers
343 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
203 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
vote
5answers
369 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
68 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
59 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
130 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
180 views

Finding large prime gaps

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

Something wrong with FromDigits?

NestList[RotateLeft, IntegerDigits[19], 1] FromDigits[%] (* WRONG *) ...
0
votes
1answer
213 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
378 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
98 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
318 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
401 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
67 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 ...
-3
votes
1answer
156 views

Miller-Rabin algorithm [closed]

I want to implement the Miller-Rabin algorithm in Mathematica to check if a number is prime with at least 99.99% probability. I used this: ...
-1
votes
1answer
188 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
298 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
753 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
113 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
278 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
80 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
105 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 $100$....
7
votes
2answers
395 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 $x\...
11
votes
4answers
587 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
227 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 ...
15
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
137 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
215 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
151 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
191 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 \sqrt{3}}{...
15
votes
4answers
3k 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
213 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
164 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 ...