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)

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

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

dCode retains ownership of the source code of the script Primorial online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Primorial script for offline use on PC, iPhone or Android, ask for price quote on contact page !