### Introduction

This is a private homepage without any purpose.
I am aware of the little mathematical importance of any of the numbers and of any of the found factors.

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

After a longer break I try to find factors of that numbers, taking the database of Markus Tervooren as source of needed information.

A smaller part of my finds is reported to Kurt Beschorner already.

The remaining part is collected in this plain text file (Aug 15, 2023).

New finds are collected here (Aug 20, 2023).

Newer finds are collected here (Sep 10, 2023) and here (Nov 23, 2023).

Latest finds (Nov 30, 2023).

A short note.
People maintaining lists of factorizations of $10^n+1$-numbers take care of so called $L$- and $M$-values
useing equations such as $10^{20k-10}+1 = (10^{4k-2}+1)$ · $L_{20k-10}$ · $M_{20k-10}$, where
$L_{20k-10}=A_{20k-10}-10^k$ · $B_{20k-10}$ and $M_{20k-10}=A_{20k-10}+10^k$ · $B_{20k-10}$ with
$A_{20k-10}=10^{8k-4}+5$ · $10^{6k-3}+7$ · $10^{4k-2}+5$ · $10^{2k-1}+1$ and
$B_{20k-10}=10^{6k-3}+2$ · $10^{4k-2}+2$ · $10^{2k-1}+1$.
But I will not do so. For my purposes it is not necessary and not helpful.

Playing with the database, I detected many factors which were uploaded by anonymous finders.
In case of interest I collected the factors in this plain text file (Aug 15, 2023).
More finds by Anonymous are collected here (Aug 20, 2023) and here (Sep 10, 2023).

### Numbers of the form $10^n-1$

My finds (not reported to Kurt Beschorner already) are collected in this plain text file (Aug 15, 2023).

New finds are collected here (Aug 20, 2023).

Newer finds are collected here (Sep 10, 2023) and here (Nov 23, 2023).

Latest finds (Dec 7, 2023).

Again I detected many factors which were uploaded by anonymous finders.
In case of interest I collected the factors in this plain text file (Aug 15, 2023), too. More finds by Anonymous are collected here (Sep 10, 2023).

10^1599-1: p55=2862577930401391395910619889316394633711512313018581507 (Aug 18, 2023; sigma=6089901937320443; B1=11000000; B2=93177894810)

### Proven primes of the form 10^n+1 or 10^n-1

In rare cases it luckily happens that after finding a factor the remaining cofactor is prime.
If this cofactor is large, then its primality is not obviously but has to be proved.
In some cases I did this using the program primo of Marcel Martin, see the table below.
The corresponding certificates are uploaded to and verified by the database.

NumberDigits
10^5990+1, L-value2355
10^3963+12579
10^2942+12885
10^7550+1, M-value2943
10^5139+13371
10^5367+13549
10^5195+14113
10^6981+14230
10^7503+14755
10^5009-14933
10^6275-14936
10^5387-15266
10^5587-15333
10^15890+1, L-value5397
10^7565+15579
10^9333+15691
10^16150+1, L-value5721
10^7337-16125
10^17450+1, M-value6929
10^7871-17351
10^8209-18162
10^14691+19453
10^9736+19665
10^17193+110355
December 9, 2023
Alfred Reich
To be extended