# Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

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### 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 ...
12k 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 ...
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 ...
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 ...
34k views

### List of first n prime numbers most efficiently and in shortest code [closed]

Rules are simple: First n primes (not primes below n), should be printed to standard output separated by newlines (primes should be generated within the code) primes cannot be generated by an inbuilt ...
9k views

### List Prime Numbers [duplicate]

Introduction Prime numbers are simple, right? Well, now you get your chance to find out! Challenge You must write a program or function that takes an input n and ...
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 ...
5k views

### Coprimes up to N

Given a number n >= 2, output all the positive integers less than n where gcd(n, k) == 1 (...
3k views

### Sum of primes between given range

Write the shortest code for finding the sum of primes between a and b (inclusive). Input a ...
1k views

### Prime factors buddies

Given an integer N > 1, output all other numbers which prime decompositions have the same digits as the prime decomposition of ...
2k views

### What is the average of n, the closest prime to n, the square of n and the closest Fibonacci number to n?

This is a math problem which takes quite many things into question, making it rather challenging, and as you might have guessed, it's a code golf, so it should be as short as possible as well. The ...
3k 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 ...
2k views

### Find largest prime which is still a prime after digit deletion

Over at https://math.stackexchange.com/questions/33094/deleting-any-digit-yields-a-prime-is-there-a-name-for-this the following question is asked. How many primes are there that remain prime after you ...
14k views

### Fastest semiprime factorization

Write a program to factorize a semi-prime number in the shortest amount of time. For testing purposes, use this: 38!+1 (523022617466601111760007224100074291200000001) It is equal to: ...
6k views

### Calculate Phi (not Pi)

No, I don't mean ϕ = 1.618... and π = 3.14159.... I mean the functions. φ(x) is the number of integers less than or equal to <...
2k views

### Is it a prime? w/o math [closed]

Write a program or function in any language that tells if the input is a prime number. The input is a string representing a natural number in base-10. The output is one of the two strings "Prime" or "...
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 ...
1k views

### Find prime factors [duplicate]

A whole program to find the prime factors of a given number. The number will be given on standard input.
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-...
2k views

### Show Ulam's spiral

Similar to this but in this one you need to write spiral starting from the center where: space means composite number .(dot) means prime number. Size of the ...
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 ...
2k views

### Prime Factoral Roots

Inspired by digital roots, the prime factoral root of a number is the number that emerges when you take the prime factors of a number, add them together, and repeat the process on the resulting number,...
1k views

### Return the first N primes

With a twist; your algorithm has to be less complex than O(X2) where X is the Nth prime. Your solution post should include the character count and the theoretical complexity in terms of X (or N, which ...
10k views

### Calculate the number of primes up to n

π(n) is the number of primes less than or equal to n. Input: a natural number, n. Output: π(n). Scoring: This is a fastest-code challenge. Score will be the sum of times for the score cases. I ...
5k views

### Find the largest prime whose length, sum and product is prime

The number 113 is the first prime whose length 3 is prime, digital sum 5 = 1 + 1 + 3 is ...
1k 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 ...
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 ...
3k views

### The Möbius Function

The Möbius Function The Möbius function is an important number theoretic function. Your submission should accept a positive integer n and return the value of the ...
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 ...
3k views

### Find the largest fragile prime

Consider the function Remove(n, startIndex, count) that removes count digits from the number ...
2k views

### Triangular Ulam spiral

We've had a couple of challenges about the Ulam spiral. But that's not enough. In this challenge we will plot a triangular Ulam spiral (as opposed to the usual, square Ulam spiral). Here's a sketch ...
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 ...
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, ...
2k views

### Recover the mutated source code

In a very unusual accident involving a small sample of radium, an electrocuted whale, and three gummy bears, some of The Management™'s source code has been mutated. Little does The Management™'s boss ...
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 ...
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, ...
970 views

### Am I a Sophie Germain prime? [duplicate]

A Sophie Germain Prime is a prime number P such that 2P+1 is prime as well. Given a prime number as input, your task is to determine whether it is a Sophie Germain Prime. Standard Input/Output rules ...
818 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 <...
370 views

### Encode Factor Trees [duplicate]

I once saw on the xkcd fora a format for expressing numbers in an odd way. In this "factor tree" format: The empty string is 1. Concatenation represents multiplication. A number n enclosed in ...
699 views

### Divisor sum from prime-power factorisation

The task is to compute the divisor sum of a number given its prime factorisation. Input Two arrays (or something equivalent) of length n, one containing the prime factor and the other containing the ...
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 ...
1k views

### Evaluate the primorial of a number [duplicate]

The primorial of a number is the product of all the primes until that number, itself included. Take a number from STDIN as the input and evaluate its primorial, ...
3k views

### Output the PPCG Prime

This is the PPCG Prime 624 digits long ...
16k views

### Fastest code to find the next prime

The problem is as follows. Input: An integer n Output: The smallest prime bigger than n. The challenge is to give the ...
1k views

### Stuffing primes in a box

Your task is write a program or function that can fill a given rectangle with prime numbers. The width and height of the ...
2k views

### Prime counting function

Introduction The Prime Counting Function, also known as the Pi function $\pi(x)$, returns the amount of primes less than or equal to x. Challenge Your program will take an integer x which you ...
4k views

### Is it a Sphenic Number?

A Sphenic Number is a number that is the product of exactly three distinct primes. The first few Sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114. This is ...
2k views

### Find the largest gap between good primes

Following the fine tradition of questions such as Find the largest prime whose length, sum and product is prime , this is a variant on a largest prime challenge. Input Your code should not take any ...