# Questions tagged [primes]

For challenges about identifying and manipulating prime numbers

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### Find the nth Mersenne Prime

A number is a Mersenne Prime if it is both prime and can be written in the form 2m-1, where m is a positive integer. For example: 7 is a Mersenne Prime because it is 23-1 11 is not a Mersenne Prime ...
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### Generate Fibonacci Primes Quickly

Unsurprisingly, fibonacci primes are primes that are also Fibonacci numbers. There are currently 34 known Fibonacci primes and an additional 15 probable Fibonacci primes. For the purpose of this ...
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### How many Sieve of Eratosthenes hits?

Sieve of Eratosthenes is a method for finding prime numbers: take the sequence of all positive integer numbers starting from 2 then for each remaining number drop all its multiples. ...
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### Long period primes

A long period prime is a prime number $p$ such that decimal expansion of $1/p$ has period of length $(p-1)$. Your task is to output this number sequence. For purposes of this challenge we will ...
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### Factorials of primes decomposition

You have to decompose a positive integer/fraction as a product of powers of factorials of prime numbers. For example ...
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### Golf the prime numbers in Shue

I'd like to introduce a new? programming language I call Shue (Simplified Thue). It has very simple syntax. Here is a program that checks if an input is divisible by three: ...
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### Prime a*b+c of N

Given an integer $N$, print or return integers $a$, $b$, and $c$ that satisfy all of the following conditions, if such integers exist: $a \times b + c = N$ $a$, $b$, and $c$ are all ...
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### High throughput prime numbers

This challenge is inspired by the High throughput Fizz Buzz challenge. The goal Generate a list of prime numbers up to 10,000,000,000,000,000. The output of primes should be in decimal digits followed ...
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### Write the most optimized assembly program to detect a prime number (from a bigger range!)

This is the second version of the task. The original task had a defect that the given range of integers was too small. This was pointed out by @harold that other methods couldn't defeat the way of ...
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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 $3 \bmod 4$. ... 778 views

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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: ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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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### Letters associated with prime numbers

If we assign each letter a respective integer, starting from 1, then a is 1, b is 2, c is 3, and so on. After z, the letters loop back around, but with a in front (aa, ab, ac). It then goes to ba, bb, ...
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