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.

It was exactly 5 years ago today, July 19, 2015 (also a Sunday!) that I invented my first googolism (the hypermega), which I would not tell this site about until January 2020.

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 like 5 gigabytes of my 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.

And when I "shifted goalposts", I wasn't actually saying "no, you're wrong", at least not intentionally. I was actually saying the user was partially correct, but I was right in the case that I was considering. I just didn't convey it that way.

I also have found myself taking a number of actions that other users on here haven't really liked. I still feel it's okay to just add things to blog posts without crediting anyone (or whatever I'm supposed to say), like the incident today (6/14) with the Mathematica code for first digits. What, exactly, am I supposed to say after adding something to a blog post?

Things I learned from my past failure:

Giving finitely many examples of a statement does not prove the statement.

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

And, finally, I should always say something if I add something in a blog post that had been discussed in the comments.


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