Primorial

The term primorial refers to two separate definitions/formulae according to some uses:

(1) Primorial defined as the product of all prime numbers inferior or equal to $ n $ is a multiplication conditioned par a primality test of the numbers inferior or equal to $ n $, see OEIS here (link)

Example: $ 6\# = 2 \times 3 \times 5 = 30 $

(2) Primorial defined as a product of the $ n $ first primes is equivalent to a multiplication of the list of the first $ n $ prime numbers, see OEIS here (link)

Example: $ 4\# = 2 \times 3 \times 5 \times 7 = 210 $

The primorial of p is written with the character sharp: p# or $ p\# $

By convention $ 1\# = 1 $

The primorial function is the function that at a natural integer $ n $ associates the value $ n\# $

The primorial calculation is a succession of multiplication of prime numbers. According to definitions (1) and (2):

Example:

Lists (1) and (2) contain the same numbers but (1) have repeated elements.