Why does this website exist?
This is a personal website, mainly summarizing my efforts on factoring (very) large numbers.
None of these factorizations has any (mathematical) reason or need.
After a longer break I decided to focus on numbers of the form 10^n+7 with n ≤ 10000.
I definitely stopped every effort on factoring any other number.

April 1, 2020.

Numbers of the form (41k^2)^41−1, k≤1000
Primarily in order to test the technical correctness of my understanding of factorizations of type
Aurifeuillian, I fully factored those 1000 numbers. More

March 27, 2019.

Numbers of the form z^41−1, z≤7000
Long ago I tried to factor some of these numbers.
Final and (some) older results (with larger z, too).

April 1, 2020.

95153^41−1 (personal P−1 record)
Using the P−1 method I found a 57-digit prime factor of 95153^41−1. It is my largest P−1 found (yet) and
still listed in the table Record Factors Found By Pollard's p-1 Method, maintained by Paul Zimmermann.

July 17, 2020.

6571^41−1

(personal P+1 record)
Using the P+1 method I found a 51-digit prime factor of 6571^41−1. It is my largest P+1 found (yet) and
still listed in the table Record Factors Found By The p+1 Method, maintained by Paul Zimmermann.

July 17, 2020.

10^14600+7 is prime
Henri Lifchitz & Renaud Lifchitz
report this number as discovered as probable prime by Patrick de Geest in 01/2005. Using the primality proving program primo (Marcel Martin)
on a CPU Intel Core i9-9940X 14x 3.30GHz machine I created a certificate
for its primality. The running times were 900,869s (wall-clock) and 22,995,787s (processes).

July 19, 2020.

10^9664+7 is factored
72367, 84449, 613295783, 10561035983 and 24355579957738977158088637 are the smaller factors.
The remaining 9611-digit factor is proven prime by certificate.
Running times: 131,056s (wall-clock) and 3,277,595s (processes).

July 21, 2020.

10^7847+7 is factored
43, 8167 and 1643468077027722466601484269 are the smaller factors.
The remaining 7815-digit factor is proven prime by certificate.
Running times: 45,069s (wall-clock) and 1,134,788s (processes).

July 22, 2020.

10^6590+7 is factored
379 and 541019600749718277218092010951 are the smaller factors.
The remaining 6558-digit factor is proven prime by certificate.
Running times: 21,613s (wall-clock) and 521,733s (processes).

July 27, 2020.

10^868+7 is factored
23, 499901574811, 1703009808217, 19616802743773 and 16076907010649457736321565809442154487219 are the smaller factors.
The remaining 790-digit factor is proven prime by certificate.
Running times: 15s (wall-clock) and 86s (processes).

July 27, 2020.

10^1315+7 is factored
9463 and 4525676981562574937994867632575528881019 are the smaller factors.
The remaining 1272-digit factor is proven prime by certificate.
Running times: 47s (wall-clock) and 568s (processes).

July 28, 2020.

10^1525+7 is factored
174573645929101, 34709361636856807877, 159857707400841813593 and 221429323335767006109006836623063 are the smaller factors.
The remaining 1439-digit factor is proven prime by certificate.
Running times: 81s (wall-clock) and 1094s (processes).

July 28, 2020.

10^1542+7 is factored
317, 2347, 7529, 8969, 19360853272484371 and 58318285377200875996892448271 are the smaller factors.
The remaining 1484-digit factor is proven prime by certificate.
Running times: 93s (wall-clock) and 1439s (processes).

August 1, 2020.

10^1556+7 is factored
151, 33258674453, 22491719289713, 4244173186504233949 and 8066700842371909277619903575501 are the smaller factors.
The remaining 1481-digit factor is proven prime by certificate.
Running times: 88s (wall-clock) and 1406s (processes).

August 1, 2020.

10^1595+7 is factored
111425051, 684488461 and 17936176733222837841655350581608284689 are the smaller factors.
The remaining 1541-digit factor is proven prime by certificate.
Running times: 94s (wall-clock) and 1482s (processes).

August 1, 2020.

10^341+7 is factored
A P55 ecm catch completed the factorization.

August 2, 2020.

Numbers of the form 10^n±1
In the past I found a few factors of these numbers, such as

33909262597306826117 or
9563613411880480653886428115541468801 or
20843690695615778321 or
1705330654275468617 or
5481233378435339580193 or
33909262597306826117 or
197122042428567985112023 or
1609947537890351636691507761 or
57638349893121349771 or
1419460648523150689 or
11095752925475302853 or
11493924613839361 or
45260833352611441 or
976808552191012543 or
4452517147965157 or
54717973107001.

Nice finds for 10^n±1
P41=7732652742988151960568776872507813340801

with P41-1 = 2^7×5^2×7×41×383×827×1447×2909×3373×32713×159763×358234307

is a factor of the L-value of 10^41350+1 (Dec 12, 2010) or

1545055310935149081*2^15+1

is a 23-digit factor of the generalized Fermat number 10^4096+1 (??, 2007) or

Numbers of the form

a^(2^m) + b^(2^m), a>b, (a,b)=1
Inspired by the book

"Prime Numbers and Computer Methods for Factorization" of Hans Riesel I started to factor some of these numbers.
This project is closed.

More

77^128+76^128 is completely factored
2916678848147910457659\

8504809650721262320129, 15759106862794714886400255\

84145776201327193917770497 and
27087650987521650236700876377718\

40490479795642503864665716663553

are the largest prime factors.

July 19, 2020.

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Alfred Reich