Misunderstanding Euclid's argument

A common flawed presentation of Euclid's proof of the infinitude of primes is as follows:

Assume there are only a finite number of primes p1,p2,,pnp_1,p_2,\ldots,p_n. Let NN be the product of all of those primes, add to it 11 and you get a new prime number since it isn't divisible by any of the primes we listed at first. Contradiction! \Rightarrow\Leftarrow Therefore, there is an infinite number of primes.

Let q1,q2,q3, q_1, q_2, q_3, \ldots be the list of all primes (in ascending order). Your mission is to find the smallest value of q1q2q3qn+1 q_1 q_2 q_3 \ldots q_n + 1 that is not a prime.

×

Problem Loading...

Note Loading...

Set Loading...