The goal of this project is to reformat the data files from The Cunningham Project into a more machine readable JSON format listing all the prime factors in a list.

Currently the JSON files are created from data in the April 6, 2022 file at Sam Wagstaff's website (https://homes.cerias.purdue.edu/~ssw/cun/pmain422.txt)

So far, the following files are available:

pmain422_table2-.json Table 2-: factorization of $2^m-1$. Only values of $m$ where a full factorization of $2^m-1$ is known are included. Includes both odd and even values of $m$.

pmain422_table2+.json Table 2+: factorization of $2^m+1$. Only values of $m$ where a full factorization of $2^m+1$ is known are included. Includes both odd and even values of $m$.

pmain422_table2LM.json Table 2LM: factorization of Aurifeuillean factors $L$, $M$ of $2^{4k+2}+1=L\times M$ where $L = 2^{2k+1}-2^{k+1}+1$ and $M = 2^{2k+1}+2^{k+1}+1$. Only values of $m = 4k+2$ where a full factorization of both $M$ and $L$ are known are included.

Since keys in JSON are required to be strings, the values of $m$ are stored as strings in the JSON files.

For instance, the following Python code will read the file pmain422_table2-.json into a dictionary whose key-value pairs are $m$ and a list of the prime factors of $2^m-1$ with repetitions:

import json
table2mdict = dict(map(lambda x: (int(x[0]), x[1]), json.load(open('pmain422_table2-.json','r'))['table2-_data'].items()))
print(table2mdict[12])
>> [3, 3, 5, 7, 13]  # 2^12-1 = 3^2*5*7*13

The following code will return, instead of a list of prime factors, a dictionary of (prime, multiplicity) key-value pairs, similar to the output of factorint in Sympy.

import json
from collections import Counter
table2mdict2 = dict(map(lambda x: (int(x[0]), dict(Counter(x[1]))), json.load(open('pmain422_table2-.json','r'))['table2-_data'].items()))
print(table2mdict2[18])
>> {3: 3, 7: 1, 19: 1, 73: 1}  # 2^18-1 = 3^3*7*19*73

TODO:

1. include values of $m$ for which there are composite factors that have not been factored yet.
2. include other machine readable formats.