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# PrimeGrid

## Overview

PrimeGrid is a distributed computing project for searching for prime numbers of world-record size. It makes use of the Berkeley Open Infrastructure for Network Computing (BOINC) platform. As of October 2020, there are about 3,300 active participants (on about 16,000 host computers) from 89 countries, reporting about 1,860 teraflops.[1]

## Sub-projects

• Type Proth:
321 Prime Search searching for mega primes of the form 3•2n±1.
27121 Prime Search searching for primes of the forms 27•2n±1 and 121•2n±1.
Proth Prime Search: searching for primes of the form k•2n+1.
Proth Prime Search Extended: searching for primes of the form k•2n+1.
• Type Sierpiński:
Seventeen or Bust: helping to solve the Sierpiński problem.
Extended Sierpiński Problem: helping solve the Extended Sierpiński Problem.
Prime Sierpiński Problem: helping Prime Sierpiński Project solve the Prime Sierpiński problem.
Sierpiński base 5: helping to solve the Sierpiński-Riesel Base 5 Problem.
• Type Riesel:
The Riesel Problem: helping to solve the Riesel problem.
Riesel base 5: helping to solve the Sierpiński-Riesel Base 5 Problem.
• Type Fermat:
Generalized Fermat Prime Search: searching for primes of the form b2n+1.
• Type Cullen/Woodall:
Cullen Prime Search: searching for mega primes of the forms n•2n+1.
Woodall Prime Search: searching for mega primes of the forms n•2n-1.
Generalized Cullen Prime Search: searching for primes of the form nbn+1.
• Others:
AP27 Search: searching for an arithmetic progression (p+d•n) that yields primes for 27 consecutive values of n.

### Former projects

Fermat Divisor Search: searching for large prime divisors of Fermat numbers. Completed April 2021.
Wieferich and Wall-Sun-Sun Prime Search: searching for Wieferich and Wall-Sun-Sun primes. Completed December 2022.[2]
Proth Mega Prime Search: searching for primes of the form k•2n+1. Terminated in October 2023.
Sophie Germain Search: searching for primes p and 2p+1, and twin primes p and p+2. Completed in December 2023.