**104 prime-numbers questions.**

Well, it's all there in the title! I'd like to be able to plot the number of twin primes =<x. Is there an inbuilt function that can do this?

One can compute the amount of twin primes below a positive integer $n$ by using the Mathematica command (taken from OEIS A001097):
...

Imagine that I need to verify that a specific integer, like $n = 10^{1347}+3049$ is prime.ProvablePrimeQ takes a lot of time, and, even if it will eventually work ...

Edit of original post:
I've been noodling around with non-trivial zeroes of the Riemann zeta function, and in particular with the expression
$$\sum_{\rho}R(x^\rho)$$
where $R(x)$ is Riemann's ...

In the following link:
https://oeis.org/A079796/b079796.txt
we can see the first 10,000 prime numbers $p$ with the property that both
$(3p)^2 + p^2 + 3^2$
and
$(3p)^2 - p^2 - 3^2$ are primes
...

I create a list of primes in table form... How do I generate and display the difference between the prime numbers in sequence?
...

I want to find prime $p$ in form of $p=32 x+1$
How can I ask WolframAlpha for such $x$ that will fulfil this equation?
EDIT: let's say that $100$ or $n$ solutions is enough for me
EDIT2: I need x's ...

i know there is a Command in Matematica to get prime number, but i want to break down the code,here is what i got
...

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 ...

When looking at the Minimal Goldbach prime partition point {p,q} for each n; where n=10^i and i = 2,3,4,...,10; I notice that these points reside in an interval with center n/2 and radius 250:
...

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

Building on the same context of this question
Is it possible to enforce constraints on the properties of the generated prime? For example, I'm trying to find a prime $p$ in the range specified in the ...

I'm new to Mathematica so my question might be trivial.
How do I generate a $200-bit$ prime with the condition that the 10 most significant bits in its binary representation are equal to some binary ...

I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals.
For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...

Given a positive integer $n$, what is the code to list $2^{a_2}3^{a_3}\cdots p^{a_p}$, where $a_i\ge 0$ are integers, with respect to the lexicographic ordering on $(a_2,a_3,\ldots, a_p)$?
The only ...

I'd like to evaluate
$$\prod_p\left(1-\frac1p\right)$$
over the $k$ largest previous primes $p\le n/2$, where $n$ is the parameter. E.g., if $n=20$ and $k=3$, I'd like the product to be over the 3 ...

I start with:n = 2228;
m = n/2;
PreviousPrime[n_] := NextPrime[n, -1]I use NestList to build the following list:
...

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

There is a formula given at the bottom of the following webpage:
https://math.stackexchange.com/questions/288747/how-to-find-number-of-prime-numbers-between-two-integers
to calculate the number of ...

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. ...

Apologies in advance for the simplicity of the question, but I can't fathom how to write the following as a sum in Mathemaitca:
\begin{align}
&\sum_{p}^{a}\sum_{n}^{b}\text{expression}
\end{align}...

How can I express a sum indexed by primes in Mathematica? Two examples that I am interested in are
(1) where the primes go from $p=2$ to, say, $p=17$.
(2) It would also be useful to have the sum ...

Wolfram Mathworld (http://mathworld.wolfram.com/SumofPrimeFactors.html) describes a function sopfr(n), the sum of prime factors, which I currently need. This code doesn't work when I insert it in ...

I am using Mathematica 11.1 to deterministically test the primality of a set of very large numbers (i.e. more than 1000 digits). Some of these calculations (understandably) take a lot of time (several ...

I'm trying to extract from the list of the first one hundred primes those which have the form 8n+1.
I have tried using Select but this just gives me an empty list:
...

Is there a way to generate a list of parametrized length, say $L$, of integers which are relatively prime among them? I would like to take into account their word-length as well, so for example the ...

I am attempting to utilise the
Conditionfunction to replace all primes in the list by a 0.
Here are my codes:
...

Example :
$$y=x^2+x+1,$$
where
1st range: $x=$ 1 to 1,000,000;
2nd range: $x=$ 1,000,001 to 2,000,000;
3rd range: $x=$ 2,000,001 to 3,000,000.

Today I was trying to compute the value of a function in one point ($f(3594641)$) using Mathematica. The main difficulty it has is that it requires both calculating primorials (product of primes) and ...

Will Prime and PrimePi test up to 3 * 10^12? Where can I find the limits for these funtions? ...

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 ...

I would like to plot the number of Mersenne primes (primes of the form $2^n-1$) lower than a given input. I am totally noob to mathematica and I do not know where to start from.
I have tried to ...

There is an exact $n$th prime number formula from mathworld
A double sum for the nth prime pn is $$p_n=1+\sum_{k=1}^{2(\lfloor n\ln n\rfloor+1)}\Biggl[1-\Biggl\lfloor\frac{\sum_{j=2}^k 1+\lfloor s(...

In Mathematica there is a built-in function called PrimeQ which tests given input as True or ...

I have to admit that I am totally noob to mathematica, and I have a question for which I have not found any easy-to-understand answer about.
How could I calculate the number of prime numbers of a ...

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.
...

I'm quite new to Mathematica yet, so there's probably a lot of not-so-subtle problems (indeed the algorithm isn't even running yet). My goal with this algorithm is to input an integer $n$ and get all ...

I would like to find the powers of a prime in the unique prime factorization of an $n$. I want a function $f[n,p]$ such that $n,p$ are given and I need to know what the power of $p$ is. For instance
...

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 ...

How do I make the slider values in Manipulate be values that are prime numbers?
Many thanks for any assistance.
Firstly, many thanks for all your considered and rapid responses. It really is very ...

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\...

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

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:
...

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 ...

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 ...

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?

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
...

I understand the format of a proof of compositeness of an integer produced by PrimeQCertificate: it's well-documented that ...

I want to plot first 100 Prime numbers in circular format (on circular orbit) in Mathematica.
How can i do this?

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