Primorial prime


In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn.
Primality tests show that
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
, the largest known primorial prime is 1098133# − 1 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: