Googology Wiki
Register
Advertisement
Googology Wiki

View full site to see MathJax equation

A gross or great dozen is equal to 144 = 122, or one dozen dozen. [1] It is a commonly used quantity by small wholesalers.

In Czech language, 144 is called "veletucet", which means "great-twelve".

Aarex Tiaokhiao calls this number duodecimal-booiol.[2]

Furthermore, it is the largest possible number of shopping hours in most weeks in some countries, since they have laws requiring observation of a weekly rest day.

Properties[]

  • It is a composite number.
  • 144 is the smallest known integer n such that \(n^5\) can be expressed as 4 5th powers; \(27^5 + 84^5 + 110^5 + 133^5 = 144^5\). It is the first counterexample of Euler's sum of powers conjecture found with CDC 6600 computer by Lander and Parkin in 1966.[3]
  • It is the largest Fibonacci number that is also a square. Indeed, it's the largest Fibonacci number to be any perfect power.[4]Theorem 1
  • It is the smallest positive integer n for which the number nn cannot be represented in the double-precision floating-point format.
  • 5144 is the first power of 5 larger than a googol.

In chess[]

It is also the number of possible king moves in 5×5 minichess.

In radiocommunications[]

The 2-meter band starts at 144 MHz.

See also[]

Sources[]

  1. Gross
  2. Part 1 (LAN) - Aarex Googology
  3. L. J. Lander & T. R. Parkin. "Counterexample to Euler’s conjecture on sums of like powers". Bulletin of the America Mathematical Society, 1966; 72, 1079. doi:10.1090/S0002-9904-1966-11654-3
  4. Florian Luca, Yann Bugeaud, Maurice Mignotte, Samir Siksek, Fibonacci numbers at most one away from a perfect power. Elem. Math. 63 (2008), no. 2, pp. 65–75. doi:10.4171/EM/89
Advertisement