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In mathematics, Euclid numbers are integers of the form En = pn# + 1, where pn# is the primorial of pn. They are named after the ancient Greek mathematician Euclid.
The first few Euclid numbers are 3, 7, 31, 211, 2311, 30031, 510511 (sloane A006862).
They were used by Euclid in his original proof that there are an infinite number of prime numbers.
It is not known whether or not there are an infinite number of prime Euclid numbers.
See also
"Euclid number"