Googology Wiki
Googology Wiki

I'm Allam, a large number enthusiast. I first became interested in numbers in early 2014, when I was doing a spreadsheet with the names of the -illions (which is pretty much where every googologist got started). However, I started to lose interest in the fall of 2014, only to return in mid-2015, which was when I began to understand the hyperoperators. I again lost interest in numbers toward the very end of that year, only to get interested again in mid-2016, and this was when I created my website.

My new favorite 6-digit number is 275,625, the square of 525. The number remains square when any number of digits are removed from the left from 1 to 4, and even better, the square of the first 3 digits is the original number with the first digit removed. The number is also the third in a chain of squares formed by substituting the square root for the digits just before the last 3, starting with 5625 and then 75625. The chain can be continued one more time: 525625 = 7252.

I joined this wiki under the username I go by now in October 2019. I had previously joined in February 2018 (which was when I made the blog post where I defined my triangular number googolisms) under a different username, but forgot the password.

Caret-Star Notation (part 2)

Parenthesis-Block Notation

My website:

Numbers with more than 101,000,000 digits whose first digits I have calculated:

22^2^32: 31592126933723384300418482232511......... (9.3418*101,292,913,985 digits, that took approximately 5 gigabytes of my old computer's RAM)

22^1,000,000,000: 8757440542467225792810260441674... (1.388*10301,029,995 digits)

210^100,000,000: 75409728889725546188718983322351328... (3.0102999566*1099,999,999 digits)

33^2^3^3: 4784568978097791859623620098016... (2.935*1064,038,130 digits)

\(7139511 \uparrow\uparrow 3\): 4401449855525698493597...


\(2^{2^{10^7}}\): 1237104893661637273090559537131... (103,010,299 digits)

\(2^{2^{5^{10}}}\): 1669641042716410548092424573360... (3.388*102,939,745 digits)

\((5^5)^{(4^4)^{(3^3)^{(2^2)^1}}}\): 2665922026939698409681342643875789555... (101,279,837 digits)

24^6^8: 9123262522796337086008648762260... (1.18305*101,011,229 digits)


In December, I was at the center of a whole debate on here about last digits of tetrations. It all started when I added examples of first and last digits of tetrations to the article, only to watch them get removed. The same user removed many of my other contributions related to digits of numbers, and in the discussion, said that I was keeping the precise method secret.

I didn't intentionally keep the precise method secret. I merely thought that a vague explanation like "recursive modular exponentiation method" would be sufficient since the method I was talking about had been on the article before, and it works in base 10 but not in most other bases.

I have also had a reputation for shifting goalposts. Why didn't I just admit that the user was correct, and just carry on with this "No, I'm right in my case" attitude?

What I learned from my past failures:

Giving finitely many examples of a statement does not prove the statement. The statement must be verified for all values to be considered fact.

A vague explanation of a method (e. x. "recursive modular exponentiation method") is insufficient. An exact explanation

If I have something interesting to add to a discussion in a blog post, I will always put it in the comments. See the comments on my blog post from June 2020 entitled "First digits of nontrivial powers" to find how I learned this the hard way.