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5040 and other Anti-Prime Numbers - Numberphile

Numberphile

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  • Recommended by 1 person: 1 on Hacker News.
  • Presented by James Grime, mathematician

Beginner. No background in the topic needed.

2.3M views10 years ago1 recommendation

Computer scienceMath for programmers

James Grime explains highly composite numbers, also known as anti-primes, and why they are highly factorable.

Dr James Grime discusses highly composite numbers. More links & stuff in full description below ↓↓↓ Continues and extra footage: youtu.be/PF2GtiApF3E Prime numbers (more videos): bit.ly/primevids Audible: audible.com/numberphile (free trial) Support us on Patreon: patreon.com/numberphile NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9 Numberphile T-Shirts: teespring.com/stores/numberphile Other merchandise: store.dftba.com/collections/numberphile

Why it's here

1 person recommends this

What people say. Recommended as an engaging introduction to highly composite numbers and their mathematical properties.

Balgairon Hacker News • Recommends

On “The fifth hyperfactorial: 5⁵×4⁴×3³×2²×1¹=86400000 milliseconds is exactly 1 day”

Numbers like 24, 60, and 360 are 'highly composite numbers'. Here is a GREAT video on these 'anti-prime' numbers : link to this video These anti-prime numbers were studied first by Ramanujan (of course) and conditions are that: 1) The prime factors must be consecutive (2^n X 3^m not 2^n X 5^m) 2) The powers of the prime factors must be deceasing as the prime number increases (2^4 X 3^3 not 2^1 X 3^5) 3) The numbers end with the the highest prime to the highest prime (2^4 X 3^1 not 2^3 X 3^2). Except for the numbers 2 and 4. More here: link

infogulchon Hacker News • Mentions

On “Lessons learned from sharding Postgres at Notion”

Numberphile made a video about "highly composite numbers" / "anti-primes", which are numbers that have more factors than all smaller numbers. link to this video There is an oeis sequence of them that starts "1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840...", which notably does not include 480. link

nikeeeon Hacker News • Mentions

On “Why 12 notes in Western music?”

These numbers are called "Highly Composite Numbers" 0. Basically, it is a series of numbers where each number has more factors than the number before it (and is the first number with that number of factors). As you hinted, they are especially useful if your number system does not have fractions or decimal places and you still want to divide things. You may recognize the beginning of the series: 1 2 4 6 12 24 36 48 60 120 180 240 360 720 Numberphile 1 calls them "Anti-Primes". 0: link 1: link to this video

willis936on Hacker News • Mentions

On “Decimal Time”

They're all magical because they are small. 12 is a highly factorable number and 10 is not. Ancient Greece was not ignorant of this fact. link link to this video