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. Any algorithm for the "Primorial" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "Primorial" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) or any database download or API access for "Primorial" or any other element are not public (except explicit open source licence). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Primorial" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source (Creative Commons CC-BY free distribution license).
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Primorial on dCode.fr [online website], retrieved on 2025-07-20,
