# Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

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### Cops and Robbers: Redacted Primality (Robbers' Thread)

This is the robbers' thread. The cops' thread is here. Your challenge is to take an uncracked submission from the cops' thread and try to find the original unredacted program. Please comment on the ...
619 views

### Output nearby primes

Write a program which takes an input (which may or may not be prime), and lists the immediate prime following and preceding it. Example input: 1259 Example ...
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 ...
2k views

### All primes from 0 to 1000

Is it possible to make this C code smaller? It prints out all primes from 0 to 1000. C, 89 chars ...
809 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 <...
825 views

### Finding Programs in the Primes

Let's assign the numbers 0 through 94 to the 95 printable ASCII characters: ...
1k views

### Find the craftiest prime

Intro Consider the process of taking some positive integer n in some base b and replacing each digit with its representation in the base of the digit to the right. If the digit to the right is a 0, ...
580 views

### Increasing Goldbach partitions

The Goldbach conjecture states that: every even number that is greater than 2 is the sum of two primes. We will consider a Goldbach partition of a number n to be a pair of two primes adding to n. ...
886 views

### Calculate the Kronecker symbol

Relevant links here and here, but here is the short version: You have an input of two integers a and b between negative ...
281 views

### Negative XOR primes

About a year ago you were asked to find the XOR primes. These are numbers whose only factors are 1 and themselves when performing XOR multiplication in base 2. Now were are going to spice things up ...
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-...
1k views

### Recursive Prime Factorization

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain;...
2k views

### Generate Sexy Primes

Sexy Primes are pairs of numbers (n, m) such as n and m both are prime, and ...
1k views

### Prime numbers between n and 2n [duplicate]

Bertrand's postulate states that there is always at least 1 prime number between n and 2n for all n greater than 1. Challenge Your task is to take a positive integer n greater than 1 and find all of ...
500 views

### Every nth prime number up to 8675309

Read this if you're confused. Challenge: The goal of this code-golf is based around the number 8675309... Your goal is to print out every prime number from 2 to ...
779 views

### Self-shortening Prime Tester

Let's get right in to it. Your challenge is to make a program that does these things depending on its input: If the input is a number, output "Prime" if the number is a prime number and "Not prime" ...
3k views

### Find the nth Fibonnaci Prime, in the shortest code

The challenge is rather simple: Take a positive whole number n as input. Output the nth Fibonacci prime number. Input can be ...
414 views

### Counting Eisenstein primes

Introduction Eisenstein integers are complex numbers of the form a+bω Where a,b are integers, and ...
1k views

### List prime-factorized natural numbers up to N in ascending order

For a given n list prime factorization of all natural numbers between 1 and n in ascending ...
2k views

### Code-Challenge:The Nearest Prime

Challenge In this task you would be given an integer N you have to output the nearest prime to the integer. If the number is prime itself output the number. The input N is given in a single ...
1k views

### Palindromic prime

I'm solving task, where: Input: A number as an integer. Output: The closest greater palindromic prime as an integer. I would appreciate hints how to make my solution shorter. Or directions if ...
359 views

### Keep Decoding This Number!

This challenge posed an algorithm for encoding an integer n as another integer r. What follows is a succinct explanation of that ...
380 views

### Find the numbers coprime to their decimal digits

Two numbers are coprime if their greatest common divisor is 1. Given a positive integer N, your task is to compute the first N terms of OEIS A061116, which is the sequence of positive integers ...
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 ...
2k views

### Recognize Twin Primes by Crashing [closed]

Background Story Bob was handed the following assignment for his programming class. Please note: this is not the actual challenge. Homework assignment 11: Twin primes Input: an integer ...
1k views

### Nth K-Ugly Number

Write the shortest code in any language of your choice to find the Nth K-ugly number. A K-ugly number is a number whose only prime factors are the prime numbers <= K. This K-ugly number is ...
584 views

### Output the first 200 primes using TeX

Write a plain TeX program that lists the first two hundred primes (in base-10 notation). Including external files/resources is not permitted. The output may be to the terminal, the log file, or the ...
285 views

### Number of ways to sum [1..n] with [n+1..2n] such that each sum is prime

Let n > 0. Let X = [1..n] and Y = [n+1 .. 2n]. Define ...
1k views

### Build a Primitive Root Diffuser

Introduction When a room has bare, parallel walls, it can create unpleasant repeating acoustic reflections (echoes). A diffuser is a device mounted on a wall which creates a blocky surface of many ...
2k views

### Find 10 large prime numbers with n digits

You are given n (200 ≤ n < 250) as a command line argument. Print 10 prime numbers with n digits. Your program should run under 1s and must be shorter than 5000 bytes (excluding). Sum the ...
199 views

### The Primitive and Basic Numbers

Your task is to generate the "Primitive and Basic" numbers, which are made like so: Start with 110. Take the digits of its base-1 representation (110 = 11) and interpret them as base-2 digits. This ...
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, ...
486 views

### Enumerate the primes using only unary arithmetic

Write a program which prints the sequence of prime numbers. The shortest solution wins! All numbers must have a unary representation (not just in the output, but throughout the entire program). This ...
1k 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 ...
330 views

### Build the Trinity Hall Prime

Based on this challenge and this Math.SE question. Idea originally come from a Numberphile video. The goal is to reproduce the logic of Professor McKee when he builds this prime. Your task is to ...
307 views

### Closest Woodall Prime

A Woodall Prime is a prime which can be calculated, given a positive integer n, with n * 2^n - 1. Your task is to, given a ...
230 views

### Cyclic prime number program generator

Challenge Your submission should consist of 2 or more programs each written in distinct languages. They can be arbitrarily numbered from 1 to k. Each program <...
345 views

### Goldbach's Comet

Back to back challenges I guess. Hopefully this one is more clear than the last. Background I was playing around with Goldbach's conjecture, and decided to plot evens (on the x-axis) vs the number ...
493 views

### Golf the Lucas Lehmer Primality Test

your task is to write a program that uses the Lucas-Lehmer primality test to check whether an input number is prime or not. This prime number candidate has the form ...
525 views

### Perfect, Germain, Vampire, Mersenne! (Don't forget narcissistic) [duplicate]

Six is a number perfect in itself, and not because God created all things in six days; rather, the converse is true. God created all things in six days because the number six is perfect. I am ...
189 views

### Quine with prime sourcecode character distribution constraints

Your program should take no input, and no network or other connections. Your program should output it's sourcecode. The sourcecode must consist of 3 types of characters: Numeric (0-9), Alpha (a-z|A-Z) ...
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 ...
2k views

### Illiteral Prime numbers [duplicate]

Your challenge is to write a program (full program, not a function), that will take an integer and output all prime numbers up to (including) the given integer. Output is any readable list containing ...
493 views

### List ALL prime-factorized natural numbers in ANY order

This is a variant of List prime-factorized natural numbers up to N in ascending order, but the solutions can be very different. Write a program that outputs prime factorizations of all natural ...
823 views

### Circular primes

Given a number determine if it is a circular prime. A circular prime is a prime where if you rotate the digits you still get prime numbers. 1193 is circular prime because 1931 and 9311 and 3119 are ...
382 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). ...
1k views

### Is it really a comcoin?

Very interesting background Comcoins are a currency like any other. The residents of Multibaseania (an economically robust system of city-states with very few residents in a galaxy far, far away) use ...
375 views

### Preprocessing primality

The challenge: Given an integer N, 1 < N < 2³¹, write code that uses the C preprocessor to determine whether N is prime, and produces a "Hello world" program if N is prime, or an error ...