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.

Numbers of the form 10^n+7 The table of Makoto Kamada with n ≤ 300 was the starting point. My searching range is n ≤ 10000. More.
April 1, 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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