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)
Primorial - dCode
Tag(s) : Arithmetics
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!
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
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
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 | 2 |
| 2 | 2 | 6 |
| 3 | 6 | 30 |
| 4 | 6 | 210 |
| 5 | 30 | 2310 |
| 6 | 30 | 30030 |
| 7 | 210 | 510510 |
| 8 | 210 | 9699690 |
| 9 | 210 | 223092870 |
| 10 | 210 | 6469693230 |
| 11 | 2310 | 200560490130 |
| … | … | … |
Lists (1) and (2) contain the same numbers but (1) have repeated elements.
Source code
dCode retains ownership of the "Primorial" source code. Except explicit open source licence (indicated Creative Commons / free), the "Primorial" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, 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, or API access for "Primorial" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Primorial" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Primorial on dCode.fr [online website], retrieved on 2024-11-21,
