Introduction

It gives me pleasure to factor numbers, especially large numbers.
None of my factorizations has any (mathematical) reason.

Numbers of the form $\Phi$(n,10)

Taking the list Phin10.txt (maintained by Makoto Kamada) as a starting point, I try to factor numbers of the form $\Phi$(n,10).

Factors of numbers of the form 10^n-1 are collected here.
By a stroke of good luck the factorization of 10^87323 − 1 = (99999..99999)87303 is complete:
10^87323 − 1 = 3^2 × 33909262597306826117 × PRP, where PRP means a 87303-digit probable prime number.

Some factors of numbers of the form 10^n+1 could be seen here.
I decided to forego the labeling of LM-values.

I stopped my efforts on factoring numbers of the form $\Phi$(n,10).

Recently found factors

Numbers of the form a^(2^m) + b^(2^m)

After reading some pages of the book
"Prime Numbers and Computer Methods for Factorization" of Hans Riesel
I started to factor some of these numbers.

More

Numbers of the form (41k^2)^41 − 1, 1 ≤ k ≤ 1000

Primarily in order to test the technical correctness of my understanding of factorizations of type Aurifeuillian, I fully factored that 1000 numbers.

More

Numbers of the form z^41 − 1, z ≤ 7000

Final results.

Some older results (with larger z, too).

June 11, 2019
Alfred Reich