Goliath & Leviathan Numbers - Numberphile

TL;DR

Investigating massive numbers like Goliath numbers with intriguing properties and symbols.

Transcript

this is the second in a Trilogy of videos about really big numbers and the notorious 666 it should make sense on its own but you can see links to all of them down in the description oh God is this is going to test my Bible knowledge aren't you the Goliath was I can't remember that oh his tribe I can't remember his tribe he fought David didn't he he... Read More

Key Insights

• #️⃣ Goliath numbers involve extended sequences of 666s within exponentials.
• 🤬 Legion and Leviathan numbers introduce larger magnitudes with distinct symbols.
• 🫷 Super Leviathan numbers push the boundaries of exorbitant numerical values.
• 🦻 Sterlings approximation aids in estimating the size of factorial-based numbers.
• 👷 The concept of repetitions and duplicates emerges in vast numerical constructs.
• #️⃣ Comparison with Graham's number showcases the scale of super Leviathan numbers.
• #️⃣ Exploration of apocalyptic numbers like Legions and Leviathans captivates mathematicians.

Questions & Answers

Q: What are Goliath numbers, and how are they characterized?

Goliath numbers consist of repeated strings of 666s and are of the form 2^N, with the smallest-known example being incredibly massive and challenging to find.

Q: How do Legion and Leviathan numbers compare, and what symbols represent them?

Legion numbers involve 666^666, while Leviathan numbers are 10^666 factorial, and both surpass a Google Plex in terms of magnitude and complexity.

Q: What defines a super Leviathan number, and how does it relate to other large numbers?

A super Leviathan number incorporates super factorials and towers of Leviathan numbers, surpassing even unimaginable sizes but still lesser than Graham's number.

Summary & Key Takeaways

• Goliath numbers like 666 are examined in terms of their structure and properties.

• Various super-sized numbers like Legion and Leviathan numbers are introduced.

• The concept of super Leviathan numbers is explained, showcasing unimaginably large numbers.