Googology Wiki
Googology Wiki

69 (sixty-nine) is a positive integer following 68 and preceding 70. Its ordinal form is written "sixty-ninth" or 69th.[1]

Properties[]

  • 69 is an odd composite number.
  • 69! < googol < 70!. Many scientific calculators will overflow at exactly googol, so on these calculators 69! is the maximal factorial number that can be stored.[2]
  • The sum of the divisors of 69 is 96, its digits reversed.
  • 69 is also a semiprime number.[3]

Cultural significance[]

  1. It is associated with a sex position. Often times, because of its sexual connotation, you will hear Nice after it is said, no matter the context.
  2. It is also the highest number ever given to a DTTV physical channel.

In googology[]

In Greek-based number-naming systems, 69 is associated with prefix "enneahexaconta-", and with prefix "novemsexaginti-" in Latin systems.

In other notations[]

All of these expressions in other notations are exact.

Notation Expression
Up-arrow notation \(10 \uparrow \log_{10}(69)\)
Hyper-E notation \(E\log_{10}(69)\#1, E\log_{10}(69)\)
Chained arrow notation \(10 \rightarrow \log_{10}(69)\)
BEAF \(\{10,\log_{10}(69)\}\)
Fast-growing hierarchy \(f_1^2(17.25)\), \(f_1(34.50)\), \(f_0(68)\)
Slow-growing hierarchy \(g_\omega(69)\); \(g_{69}(n)\); \(g_{\omega^{\log_{10}(69)}}(10)\)
Hardy hierarchy \(H_{\omega2}(17.25), H_{\omega}(34.50)\)

Sources[]

  1. Wolfram Alpha. Retrieved 2021-12-2.
  2. Numberphile, 69!. Accessed 2021-05-19.
  3. OEIS, Sequence A001358. Accessed 2021-05-19.