Primorial prime

In mathematics, primorial primes are prime numbers of the form p_n# ± 1, where p_n# is the primorial of p_n (the product of the first n primes).

According to this definition,

The first term of the second sequence is 0, because p₀# = 1 is the empty product, and thus p₀# + 1 = 2, which is prime. Similarly, the first term of the first sequence is not 1, as p₁# = 2, and 2 - 1 = 1 is not prime.

The first few primorial primes are

As of 28 February 2012^[ref], the largest known primorial prime is 1098133# − 1 (n = 85586) with 476,311 digits, found by the PrimeGrid project.

Euclid's proof of the infinitude of the prime numbers is commonly misinterpreted as defining the primorial primes, in the following manner:

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