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

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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.

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

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