# Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

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### Sieve of Sundaram (for finding prime numbers)

The Challenge Implement the Sundaram sieve for finding prime numbers below n. Take an input integer, n, and output the prime ...
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### Counting Cunningham chains

Prime numbers have always fascinated people. 2300 years ago Euclid wrote in his "Elements" A prime number is that which is measured by a unit alone. which means that a prime is only divisible by <...
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### Primes, as efficiently inefficient as possible [duplicate]

Write a program that tests if a number n is prime by checking that none of the integers between 2 and ...
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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 ...
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### Composite Number Sequences

Composite Number Sequences Inspired by this question Given a positive integer n, your code must output the first n composite numbers. Input / Output You may write a program or a function. Input is ...
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### 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 ...
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### A naturally occurring prime generator

There are quite a large number of prime generating functions. Pretty much all of them are constructed and are based on the sieve of Eratosthenes, the Möbius function or the Wilson's theorem and are ...
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### Puzzle: Factor these 256-bit semiprimes [closed]

Challenge Write a program to factor this set of 10 numbers: ...
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### 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 ...
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### Sum of smallest prime factors

SF(n) is a function which computes the smallest prime factor for a given number n. We'll call T(N) the sum of every SF(n) with 2 <= n <= N. T(1) = 0 (the sum is over 0 summands) T(2) = 2 (2 ...
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### Prime Nerd Sniping Pattern

Longest day of the year - here's something to waste the extra time... Overview Note this is not a popularity contest and not a graphical output challenge - you are only required to output a string ...
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### 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;...
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### 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 ...
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### List Sophie Germain primes

The Question A Sophie Germain prime is a prime p such that 2p+1 is prime as well. For example, 11 is a Sophie Germain prime because 23 is prime as well. Write the shortest program to calculate Sophie ...
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### Factoring a 64-bit integer

Write a GOLF assembly program that reads an integer from stdin (followed by a trailing newline), and outputs its prime factors seperated by newlines, followed by a trailing newline on stdout. The ...
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### Prime polynomials

Given a polynomial, determine whether it's prime. A polynomial is ax^n + bx^(n-1) + ... + dx^3 + ex^2 + fx + g, where each term is a constant number (the ...
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### 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 &...
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### Finding Programs in the Primes

Let's assign the numbers 0 through 94 to the 95 printable ASCII characters: ...
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### Finding prime numbers without using “prime characters”

Your task, if you choose to accept it, is to write a program/function that accepts an integer N as input. The program/function should output/return a list of the first N prime numbers. But here's the ...
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### 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 ...
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A curious kid uses a program which can factorize a number or an expression into the following form: p1^e1 * p2^e2 * ... * pn^en. Exponents equal to ...
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### 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 ...
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### Cops and Robbers bowling (Robbers)

Robbers' Thread In this challenge, your goal is to crack some code written by the Cops (their code is here) by modifying it. You have cracked their code if: Your modified code has a maximum ...
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### Cops and Robbers bowling (Cops)

Cops' Thread In this challenge, your goal is to write a function that accepts a integer N, and that function will return the first ...
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### 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 ...
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### Recover the mutated source code (for robbers)

This is the companion thread to the main Recover the mutated source code (link) challenge. If you have successfully cracked a cop's answer, post your solution as an answer to this question. As a ...
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### 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 ...
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### Find the largest fragile prime

Consider the function Remove(n, startIndex, count) that removes count digits from the number ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Combinatorial products of unique primes

Statement of problem Given a set of unique, consecutive primes (not necessarily including 2), generate the products of all combinations of first powers of these primes — e.g., no repeats — and also 1....
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### Anagramming Code

Let's try this again. The object of this contest is to make two pieces of code that are anagrams of each other (the two must contain the same bytes in a different order), and they will do the ...
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### These Primes of Mine Are Always Solid Lines

Let's create a N×N grid of spaces and underscores that can be used to visually determine if a number is prime. (N may be any positive integer.) This grid has three simple rules: The nth column ...
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### 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 ...
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### 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, ...
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### Primality Testing in Manufactoria

Background Manufactoria is a game about programming. The player must use a form of two-dimensional programming language to complete tasks. If you've never heard of it, the easiest way to learn is to ...
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### is_gaussian_prime(z)?

Task Write a function that accepts two integers a,b that represent the Gaussian integer z = a+ib (complex number). The program ...
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### Find prime which is generating longest primes sequence using p(n+1)=(p(n)^2+1)/2

Consider following recurrence relation: p[n + 1] = (p[n]^2 + 1) / 2 If p, p, ..., <...
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### 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 ...
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### 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 change ...
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### Determine if a number is prime without using arithmetic [duplicate]

Write a program which determines if a given number is prime. The catch: No digits or arithmetical operators. This means: No digits from 0 to ...
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### Calculate prime gaps

Finding primes is a programming rite of passage and very frequently a first serious program someone crates (usually with trial division). But primes alone are already worn out. A next far more ...
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### 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 ...
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### 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 ...
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### 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 "...
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### Goldbach's conjecture

Write a program that prompts the user for an even integer greater than 2. Given Goldbach’s conjecture that every even integer greater than 2 can be expressed as the sum of two primes, print out two ...
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### 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) ...