Euclid numbers

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The Euclid numbers belong to an infinite coprime sequence, thus implying that there are an infinite number of primes.

$E_{n}:=1+{p_{n}}\#=1+\prod _{i=1}^{n}p_{i},\quad n\geq 0,\,$

where $\scriptstyle {p_{n}}\#\,$ is the $\scriptstyle n\,$th primorial number, $\scriptstyle p_{i}\,$ is the $\scriptstyle i\,$th prime and for $\scriptstyle n\,=\,0\,$ we get 1 + (empty product, i.e. 1) = 2.

Euclid numbers (quasi primorial numbers): 1 + product of first $\scriptstyle n\,$ consecutive primes. (Cf. A006862)

{2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, 6469693231, 200560490131, 7420738134811, 304250263527211, 13082761331670031, 614889782588491411, 32589158477190044731, 1922760350154212639071, ...}