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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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)

Answers to Questions

What is a primorial? (Definition)

The term primorial refers to two separate definitions/formulae:

(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.

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 primes.

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:

n

n# (1)

n# (2)

1

1

1

2

2

2

3

6

6

4

6

30

5

30

210

6

30

2310

7

210

30030

8

210

510510

9

210

9699690

10

210

223092870

11

2310

6469693230

...

...

...

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

Source code

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