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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#




Answers to Questions (FAQ)

What is a primorial? (Definition)

The term primorial refers to two separate definitions/formulae according to some uses:

(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 $, see OEIS here (link)

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 $ prime numbers, see OEIS here (link)

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)
112
226
3630
46210
5302310
63030030
7210510510
82109699690
9210223092870
102106469693230
112310200560490130

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

Source code

dCode retains ownership of the online "Primorial" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Primorial" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Primorial" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Primorial" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

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Questions / Comments

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