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, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

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)

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 \( 1\# = 1 \)

The primorial function is the function that at a natural integer \( n \) associates the value \( n\# \)

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.

dCode retains ownership of the source code of the script Primorial online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Primorial script for offline use on PC, iPhone or Android, ask for price quote on contact page !

primorial,prime,product,p,sharp

Source : https://www.dcode.fr/primorial

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback