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Primorial

Tool to compute a primorial. Primorial n# is the product of all prime numbers inferior or equal to n, or the product of all n first prime numbers (it depend on the selected definition)

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Primorial -

Tag(s) : Arithmetics

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# Primorial

## Primorial Calculator N#

 Definition Product of all prime numbers inferior or equal to N Product of the N first prime numbers

### What is a primorial? (Definition)

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 $1\# = 1$

### What is the primorial function?

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

### How to calculate a primorial?

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

Example:

nn#
(1)
n#
(2)
112
226
3630
46210
5302310
63030030
7210510510
82109699690
9210223092870
102106469693230
112310200560490130

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

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Primorial on dCode.fr [online website], retrieved on 2023-10-01, https://www.dcode.fr/primorial

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