### Introduction

This is a personal website.

Its aim is to find some factors of somewhat larger numbers,

which are taken from the database of Markus Tervooren

and where any result is uploaded to.

### Numbers of the form 10^n + 1

Finds in 2023: 6583 factors of 5752 numbers (Dec 28, 2023).

The largest factor is p42 = 713179443752745679211641547767533209753303 of 10^839 + 1.

(10^183917+1)/11/9952852373 is a probable prime with 183906 digits (February 9, 2024).

(10^313741+1)/11/11294677 is a probable prime with 313733 digits (April 15, 2024).

### Numbers of the form 10^n − 1

Finds in 2023: 2389 factors of 2305 numbers (Dec 28, 2023).

The largest factor is p55 = 2862577930401391395910619889316394633711512313018581507 of 10^1599 − 1.

### Proven primes (related to numbers of the forms 10^n ± 1)

For a large number it is not easy to determine wether it is prime or composite.

Marcel Martin wrote the program primo which can prove (or disprove) the primality of a number.

In a few cases I used it to create a certificate (Dec 25, 2023).

April 15, 2024

Alfred Reich