grellgond 0.1.2

Official library for ℷ (The Grellgond mathematical constant)

The Grellgond Constant (ℷ)

The Grellgond constant (symbol: ℷ, 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 ℷ is defined as the concatenation of the base-10 digits of the sequence G, prefixed by 0.:

ℷ = 0.12468141820223436...

Installation

You can install the official calculation library via pip:

pip install grellgond

Usage

In Python

from grellgond import gimel

# Print the constant (pre-calculated approximation)
print(gimel)
# Output: ℷ (Grellgond Constant) ≈ 0.1246814182022343644

# Dynamically calculate exact digits up to a prime limit
exact_digits = gimel.calculate_digits(prime_limit=100000)
print(exact_digits)

Command Line Interface (CLI)

After installing, calculate the constant directly from your terminal:

grellgond --limit 100000

Authors

Created and formalized by Simon and Viliam.