Euclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set p_1, p_2, p_3,...p_n. Compute N = p_1 p_2 p_3...p_n + 1. This number N is either prime or composite.
If it is prime, then the original supposition that the primes form a finite set is false. For example, if we assume that the only primes are 2, 3, and 5, then N = 31, which is prime. Therefore, 31 should be in the set of primes.
If N is composite, then there must be another prime number because N is not divisible by any of the primes in the original set. For example, if we assume the only primes are 2, 3, 5, and 31, then N = 931 = 7^2 19. Therefore, 7 and 19 should be in the set as well.
Either way, a contradiction is reached, and the set of primes must be infinite. In other words, we can always add another prime to the set.
Write a function to return the nth Euclid number p_1 p_2 p_3...p_n + 1 as a character string, where is the nth prime. Take the zeroth Euclid number to be 2.
Solve

Solution Stats

24 Solutions

10 Solvers

Last Solution submitted on Dec 14, 2025

Last 200 Solutions

Solution Comments

Show comments

Problem Recent Solvers10

George Berken Christian Schröder GeeTwo Jayden

Suggested Problems

More from this Author323

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!