# Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

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12answers
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### Ravenity of Cube Distance Numbers

Inspired by this Numberphile entry Background The cube distance numbers of an integer n are defined here as the set of integers that are x³ distance away for a given x. For a simple example, with <...
40answers
5k views

### 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 ...
28answers
2k views

### Magnanimous numbers

Given an positive integer as input determine if it is a magnanimous number. A magnanimous number is a number such that any insertion of a + sign between any two ...
287answers
44k views

### Is this number a prime?

Believe it or not, we do not yet have a code golf challenge for a simple primality test. While it may not be the most interesting challenge, particularly for "usual" languages, it can be nontrivial in ...
20answers
1k views

### Sum pyramid of primes

Given a number N, the challenge is to get the sum of the pyramid of N primes. To clarify things, here is an example: Input: 4 We will list the first ...
15answers
1k views

### Am I a Pillai prime?

A Pillai prime is a prime number $p$ for which there exists some positive $m$ such that $(m! + 1) \equiv 0 \:(\text{mod } p)$ and $p \not\equiv 1\:(\text{mod }m)$. In other words, an ...
3answers
100 views

### 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 (...
12answers
1k views

### Find the Emirps!

An emirp is a non-palindromic prime which, when reversed, is also prime. The list of base 10 emirps can be found on OEIS. The first six are: ...
21answers
1k views

### Primenary Strings

A Primenary (binary-prime) string is one which, when written as a binary grid, every row and column has a prime total. That's quite a vague explanation, so let's break it down with a worked example.....
12answers
3k views

### 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. ...
17answers
1k views

### Counting +1 primes

Define that the natural number p is a +1 prime of the natural number n if p is a prime number and the standard binary representation (i.e., without leading zeroes) of p can be obtained by adding (i.e.,...
18answers
1k views

### Square-free semiprime counting

Definition A square-free semiprime is a natural number that is the product of two distinct prime numbers. The task Given a natural number n, count all square-...
103answers
11k views

### List of primes under a million

This is my first code golf question, and a very simple one at that, so I apologise in advance if I may have broken any community guidelines. The task is to print out, in ascending order, all of the ...
16answers
3k views

### ​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 $x = 2+y$ ...
17answers
4k views

### Primes other than Optimus

Challenge Given an input integer n > 0, output the number of primes (other than n, if n ...
23answers
3k views

### Find the prime factors

In this task, you have to write a program, that computes the prime factors of a number. The input is a natural number 1 < n < 2^32. The output is a list of the prime factors of the number in the ...
10answers
385 views

### 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). ...
11answers
2k views

### Encode an integer

Given positive integer n > 2. We convert it to an array as follows: If it is equal to 2 return an empty array Otherwise ...
17answers
1k views

### Primes in the prime factorisation

I saw another prime challenge coming by in PPCG, and I do love me some primes. Then I misread the introductory text, and wondered what the creative brains here had come up with. It turns out the ...
13answers
679 views

### Goldbach partitions

The Goldbach conjecture states that every even number greater than two can be expressed as the sum of two primes. For example, 4 = 2 + 2 6 = 3 + 3 8 = 5 + 3 ...
2answers
886 views

### 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 ...
18answers
9k views

### The prime ant 🐜

The "prime ant" is an obstinate animal that navigates the integers and divides them until there are only primes left! Initially, we have an infinite array A containing all the integers >= 2 : ...
9answers
1k views

### Repeated Digit Primes

Another sequence, another challenge.* Definition A prime p is in this sequence, let's call it A, iff for every digit ...
20answers
3k views

### Is it a Chen prime?

A number is a Chen prime if it satisfies two conditions: It is prime itself Itself plus two is either a prime or a semi-prime. A prime is a number where it has exactly two divisors and those ...
16answers
2k views

### Sort a number's divisors by prime factorization

Given an input of an integer ≥ 2, output a list of its divisors sorted by the exponents in their prime factorizations, in ascending order, ordering first by the largest prime, then by the second ...
16answers
1k views

### Prime Powers of Primes

For the purpose of this challenge, a Prime Power of a Prime (PPP) is defined as a number that can be defined as a prime number to the power of a prime number. For example, 9 is a PPP because it can ...
6answers
2k views

### 1, 2, 3, 14… or is it 15?

A well known song by the Irish rock band U2 starts with the singer Bono saying "1, 2, 3, 14" in Spanish ("uno, dos, tres, catorce"). There are various theories as to the significance of those numbers....
22answers
2k views

### Is it a weak prime?

A prime is weak if the closest other prime is smaller than it. If there is a tie the prime is not weak. For example 73 is a weak prime because 71 is prime but 75 is composite. Task Write some ...
9answers
3k views

### Closest 7-Distinct-Prime Product

(via chat) The OEIS entry A123321 lists the sequence of numbers that are the product of seven distinct primes. For brevity, we'll call this a 7DP number. The first few numbers and their corresponding ...
14answers
1k views

### Generate n-ary numbers

A secondary number is a positive integer whose prime factors (without multiplicity) are all less than or equal to its square root. 4 is a secondary number, because ...
28answers
2k views

### Largest Prime Exponents

Given an integer n >= 2, output the largest exponent in its prime factorization. This is OEIS sequence A051903. Example Let ...
33answers
2k views

### Calculate the prime factors

We had a prime factorization challenge a while ago, but that challenge is nearly six years old and barely meets our current requirements, so I believe it's time for a new one. Challenge Write a ...
19answers
3k views

### Print the nth prime that contains n

This question will be a twist on finding the nth prime number. Challenge You must write a program that will take one input n, ...
28answers
2k views

### Array Factorization

Given an array of positive integers, output a stable array of the distinct prime factors of these integers. In other words, for each integer in the input in order, get its prime factors, sort them, ...
34answers
3k views

### Is it a Mersenne Prime?

A number is a Mersenne Prime if it is both prime and can be written in the form 2n-1, where n is a positive integer. Your task is to, given any positive integer, determine whether or not it is a ...
14answers
2k views

### Prime containment numbers (golf 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 ...
21answers
3k views

### Bertrand's Primes

Bertrand's Postulate states that for every integer n ≥ 1 there is at least one prime p such that n < p ≤ 2n. In order to verify this theorem for n < 4000 ...
39answers
12k views

### Find the Smoothest Number

Your challenge is to find the smoothest number over a given range. In other words, find the number whose greatest prime factor is the smallest. A smooth number is one whose largest prime factor is ...
12answers
2k views

### Shortest code to find next prime palindrome

I was trying to find the shortest code possible that given a number n, returns the next prime palindrome number (limited to below 100000). If the number itself is a prime palindrome, the code should ...
25answers
4k views

### The program that will find the next prime number

Intro: You accidentally corrupted the flow of time with a device you made for fun, that turned out to be a time machine. As a result, you got pushed to the far future. You realized that computing, ...
19answers
2k views

### Is this a consecutive-prime/constant-exponent number?

A while ago, I had a look at the prime factorization of 27000: 27000 = 23 × 33 × 53 There are two special things about that: consecutive-prime: The primes are consecutive: 2 is the ...
27answers
2k views

### Prime or highest factor

Challenge: Given an array of non-negative whole numbers numbers in the range of 0 to Infinity, Check whether all of them are primes or not. (You can take input as ...
7answers
811 views

### Golf the pseudoprimes!

Introduction / Background In a recent discussion in the crypto chat I was challenged to discuss / help with the Fermat primality test and Carmichael numbers. This test is based on the premise that <...
21answers
1k views

### Excessive Integers

For a positive integer n with the prime factorization n = p1^e1 * p2^e2 * ... pk^ek where ...
31answers
2k views

### Finding Not-Quite-Prime Numbers

Your challenge, should you chose to accept it, is to code-golf a function that returns true or false (or some similar meaningful representation of yes and no) if a number meets the following criteria: ...
9answers
834 views

### Pair-golfing Twin primes and the Collatz sequence

This is a new kind of challenge inspired by the Recover the mutated source code problem. You should write two programs or functions both in the same language. The first one should solve Task #1 and ...
17answers
1k views

### Find the smallest prime from a substring

In 1946 Erdos and Copeland proved that a certain number is a normal number, i.e. the digits in its decimal expansion are uniformly distributed. Users will input a sequence of digits and you will find ...
33answers
3k views

### Calculate the sum of the first n prime numbers

I'm surprised that this challenge isn't already here, as it's so obvious. (Or I'm surprised I couldn't find it and anybody will mark it as a duplicate.) Task Given a non-negative integer $n$, ...
22answers
6k views

### Can even numbers become prime?

The Sequence Everyone knows the only even prime number is 2. Ho-hum. But, there are certain even numbers n where, when ...
13answers
2k views

### Fond Memories of Past Primes

Consider a prime number p, written in base 10. The memory of p is defined as the number of distinct primes strictly less than p that are contained as substrings of p. Challenge Given a non-negative ...