# Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

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### Is it a Giuga number?

Giuga numbers (A007850) are composite numbers $n$ such that, for each prime factor $p_i$ of $n$, $p_i \mid \left( \frac n {p_i} -1 \right)$. That is, that for each prime factor $p_i$, you ...
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### Recognize most smaller primes with a regex

This time, you are working on a regex. Your regex is meant to approximately full-match the base-10 representations of primes $0 \le p < 1000$, while ignoring any non-numeric string or composite ...
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### No of subsets of a given array such that their product is in the form of p1*p2*p3 [closed]

Given an array $A$ of size $n$. You have to find the number of subsets such that their product is in the form of $p_1 \times p_2 \times p_3 \dots$ where $p_1, p_2, p_3, \dots$ are prime ...
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### Reconstruct a recursively prime-encoded integer

Recursively prime-encoded integers Consider $11681169775023850 = 2 \times 5 \times 5 \times 42239 \times 5530987843$. This isn't a nice prime factorisation, as $42239$ and $5530987843$ make it ...
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### Outputting Blum Integers

According to Wikipedia, In mathematics, a natural number $n$ is a Blum integer if $n = p \times q$ is a semiprime for which $p$ and $q$ are distinct prime numbers congruent to $3 \bmod 4$. ...
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### Gödel numbering of a string

Background Gödel numbers are a way of encoding any string with a unique positive integer, using prime factorisations: First, each symbol in the alphabet is assigned a predetermined integer code. Then, ...
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### Make it prime with the smallest suffix

Given a positive integer as input, output the smallest positive integer such that appending its digits (in base 10) to the end of the input number will form a prime number. Examples ...
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### Calculate Home Primes

The Home Prime of an integer $n$ is the value obtained by repeatedly factoring and concatenating $n$'s prime factors (in ascending order, including repeats) until reaching a fixed point (a prime). ...
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### Random pair of primes

Given a positive input $n$, output a random pair of primes whose difference is $n$. It's fine if there's another prime between them. Every pair should possibly appear and the program should have ...
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### Finding Distant Primes

Let us call a prime $p$ an $(m,k)$-distant prime $(m \ge 0, k \ge 1, m,k \in\mathbb{Z})$ if there exists a power of $k$, say $k^x (x \ge 0, x \in\mathbb{Z})$, such that $|k^x-p| = m.$ For ...
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### I ain't no Fortunate sum

The primorial $p_n\#$ is the product of the first $n$ primes. The sequence begins $2, 6, 30, 210, 2310$. A Fortunate number, $F_n$, is the smallest integer $m > 1$ such that $p_n\# + m$ ...
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### Reconstruct an integer from its prime exponents

All integers $n > 0$ can be expressed in the form $$n = \prod_{\text{prime } p} p^e = 2^{e_2} 3^{e_3} 5^{e_5} 7^{e_7} \cdots$$ This form is also known as it's prime factorisation or prime ...
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### Python Prime Problem [duplicate]

Your challenge is to write a Python program to print all the primes (separated by whitespace) less than a given integer N with an asterisk (...
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### Ginormous number

Output this 1364-digit base-10 number: ...
846 views

### Prime generating function

Background The Python code ((((((((n%35)^11)*195)|53)&181)+n)%168)*n)+83 produces 74 distinct primes for $0 \le n \le 73$. This code also works in Java. The ...
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### All-inclusive semi-primes

$723 = 3 \times 241$ is a semi-prime (the product of two primes) whose prime factors include all digits from $1$ to $n$, where $n$ is the total number of digits between them. Another way to ...
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### Looks prime to me!

Figuring out whether a given number is prime, while not very complicated, is kind of hard. But making a guess doesn't need to be. Seeing whether a number is a multiple of 2 or 5 is easy - you can just ...
3k views

### Shortest "arithmetic" formula to output 1000 primes

Write a formula using only the digits 0-9, +, *, -, <...
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### Delicate primes

Inspired by Find the largest fragile prime. By removing at least 1 digit from a positive integer, we can get a different non-negative integer. Note that this is different to the ...
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### Double Prime Words

Consider a word/string of length $n$, only including the letters A-Z, a-z. A word/string is a double prime word if and only if n is prime and the sum of the letters, s, is also prime, using their ...
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### Prime Power Switch

Input: A positive integer n=p^q where p and q are prime. Output: Output the result of ...
183 views

### Prime decimal representations of prime binary numbers [duplicate]

Problem Statement: Consider a number n in base-10. Find the smallest base-10 integer i greater than ...
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### Is it almost-prime?

Sandbox Definition: A positive integer n is almost-prime, if it can be written in the form n=p^k where ...
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### Prime Challenge

CODE GOLF & Coding Challenges: In today's challenge, you'll be asked to print the following very special AND tricky AND satisfying Prime Number...! Are you golfers ready? ...
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### Prime Modified Z-Factorials

Let me explain one by one the above terms... We will call $\text{Z-Factorial}(n)$ of a positive integer $n$, $n!$ (i.e. $n$ factorial) without any trailing zeros. So, $\text{Z-Factorial}(30)$...
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### Legendre's (Unsolved) Conjecture

Legendre's Conjecture is an unproven statement regarding the distribution of prime numbers; it asserts there is at least one prime number in the interval $(n^2,(n+1)^2)$ for all natural $n$. The ...
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### Find all Belphegor primes

A Belphegor number is a number of the form $(10^{n+3}+666)*10^{n+1}+1$ (1{n zeroes}666{n zeroes}1) where $n$ is an non-negative integer. A Belphegor prime is a ...
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### Generate *all* coprime tuples

Given integers k and n, generate a sequence of n unique k-tuples of pairwise coprime ...
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### Draw the prime race tracks

Odd prime numbers are either in the form of 4k+1 or 4k+3 where k is a non-negative integer. ...
315 views

### Produce all even primes

A prime number is a positive integer that has exactly two divisors 1 and the number itself. For example number 7 is a prime since it is divisible by 1 and 7. Number 1 is not a prime since it has only ...
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### Geiger counter prime generation [closed]

This challenge is quite simple to conceptualise, but likely a lot harder to execute. In this challenge, the program will have to detect the number N of its characters that have been randomly changed (...
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### Prime parity peregrination

The purpose of this challenge is to graphically depict a walk on the plane, where the direction of each step $k$ is determined by the primality of $k$ and the parity of its binary expansion. ...
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### ​Cuban​ ​Primes

Given a natural number $n$, return the $n$-th cuban prime. Cuban Primes A cuban prime is a prime number of the form $$p = \frac{x^3-y^3}{x-y}$$ where $y>0$ and $x = 1+y$ or $x = 2+y$ ...
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### Composite Factor Soup

Per the fundamental theorem of arithmetic, for a given number $n$, it is possible to find it's prime factors, and they are unique. Let's imagine we talk only of $n$ that is non-prime (composite). ...
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### Make some Prime Squares!

What is a Prime Square? A Prime Square is a square where all four edges are different prime numbers. But which ones? And how do we construct them? Here is an example of a 4x4 Prime Square ...
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### Can a neural network recognize primes?

Background Recognizing primality seems like a poor fit for (artificial) neural networks. However, the universal approximation theorem states that neural networks can approximate any continuous ...
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### Return the Closest Prime Number

Challenge This is a simple one: Given a positive integer up to 1,000,000, return the closest prime number. If the number itself is prime, then you should return that number; if there are two primes ...
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### Prime containment numbers (speed edition)

This is sequence A054261 The $n$th prime containment number is the lowest number which contains the first $n$ prime numbers as substrings. For example, the number $235$ is the lowest number ...
This is sequence A054261. The $n$th prime containment number is the lowest number which contains the first $n$ prime numbers as substrings. For example, the number $235$ is the lowest number ...