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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

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Primorial Calculator N#




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.

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)
111
222
366
4630
530210
6302310
721030030
8210510510
92109699690
10210223092870
1123106469693230
.........

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

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Source code

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