grellgond 0.1.0

Official library for ℷ (The Grellgond mathematical constant)

The Grellgond Constant (â„·)

The Grellgond constant (symbol: â„·, Gimel) is a mathematical constant defined as the decimal concatenation of the sequence of strictly increasing maximal prime gaps.

Mathematical Definition

Let $p_n$ denote the $n$-th prime number. A maximal prime gap $g_k$ is defined as a gap between consecutive primes that is strictly greater than all preceding prime gaps.

The sequence of maximal prime gaps $G$ begins: $G = (1, 2, 4, 6, 8, 14, 18, 20, 22, 34, ...)$ (OEIS A005250)

The Grellgond constant â„· is defined as the concatenation of the base-10 digits of the sequence $G$, prefixed by $0.$: $$ â„· = 0.12468141820223436... $$

Installation

You can install the official calculation library via pip:

pip install grellgond

Usage

In Python

from grellgond import gimel, GrellgondConstant

# Print the constant (pre-calculated approximation)
print(gimel)
# Output: ℷ (Grellgond Constant) ≈ 0.12468141820223436

# Dynamically calculate digits up to a prime limit
exact_digits = gimel.calculate_digits(prime_limit=1000000)
print(exact_digits)

Command Line Interface (CLI)

After installing, you can calculate the constant directly from your terminal:

grellgond --limit 100000

Authors

Created and formalized by Simon and Villiam.