Search for a tool
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)

Results

Primorial -

Tag(s) : Arithmetics, Mathematics

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Primorial tool. Thank you.

# Primorial

## Primorial Calculator N#

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

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)

### How to calculate a primorial?

The term primorial refers to two separate definitions:

'(1) Primorial defined as the product of all prime numbers inferior or equal to n is a simple 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.

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

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.

In both cases, the primorial of p is written with the character sharp: p# or $$p\#$$

By convention $$1\# = 1$$