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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

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)

### 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.

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:

 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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