A Curious Sequence of Prime Numbers

We do not know whether every prime number appears in the Euclid-Mullin sequence. The similar sequence that chooses the largest instead of smallest prime that divides 1 plus the product of the previous terms avoids an infinite number of primes. I am drawn to adorable and amusing math, so I hope the Euclid-Mullin sequence contains all prime numbers.

Source: blogs.scientificamerican.com