Meaning of primorial | Babel Free

Definitions

1. Any number belonging to the integer sequence whose nth element is the product of the first n primes.
2. A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input.

Examples

“For example, up to 10⁹, every positive integer which is a multiple of a primorial and is less than the following primorial satisfies the given inequality. There has also been little discussion on which primorials qualify in the different situations when RH fails.”

“The primorial of 6 is #92;textstyle 6#92;#35;#61;2#92;times 3#92;times 5#61;30.”

“2020, Rong Pan, Qinheping Hu, Rishabh Singh, Loris D'Antoni, Solving Problem Sketches with Large Integer Values, Peter Müller (editor), Programming Languages and Systems: 29th European Symposium, Proceedings, Springer, LNCS 12075, page 587, The following number theory result relates the primorial to the Chebyshev function. θ(n)= log (n#)= log 2⁽¹⁺ᵒ⁽ⁿ⁾⁾ⁿ=(1+o(n))n”

CEFR level