256


256 < 255 \| 257 >

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256 (two hundred fifty-six) is a positive integer equal to \(2^{8} = 2^{2^3}\).

It is found commonly in computer science, being the the number of different values expressible in 8 bits (a byte). For that reason internally stored values in a game which are not programmed to exceed a byte encounter an overflow and may either loop back to a value of 0 or glitch an aspect of the game. One instance of this is in the classic arcade game Pac-Man, which glitches out after level 255.^[1]^[2]

This number is equal to \(2\downarrow\downarrow4\) in down-arrow notation.

Alistair gave "fzfour", which equals this number, as an example after introducing his fz- prefix to his children, since it is equal to 4⁴.^[3]^[4]^[5]

Aarex Tiaokhiao calls this number hexadecimal-booiol and maser.^[6]

IsTakenIsTaken calls this number biudutremix, and it is equal to 2↑↓↑3 in Mixed arrow notation.^[7]

BlankEntity calls this number jói sá fjórði, and it's the 42nd number of Celtchar of New World. ^[8]

Oganso uses the name byte for this number.^[9]

Properties[]

Its factors are 1, 2, 4, 8, 16, 32, 64, 128 and 256, making it a composite number.^[10]^[11]^[12]
256 is an even number^[13]^[14].
256 is an unhappy number.^[15]^[16]

256 is a centered octagonal number.^[17]
256 is deficient.^[18]
Its prime factorization is 2⁸.

Approximations[]

Notation	Lower bound	Upper bound
Up-arrow notation	16 ↑ 2
Scientific notation	\(2.56\times10^2\)	\(2.561\times10^2\)
Slow-growing hierarchy	\(g_{\omega^{\omega}}(4)\)	\(g_{\omega^{\omega}}(5)\)
Copy notation	2[3]	3[3]
Chained arrow notation	16 → 2
Bowers' Exploding Array Function/Bird's array notation	{16,2}
Fast-growing hierarchy	f₂(5)	f₂(6)
Hardy hierarchy	H_ω(128)	H_ω(128)
Middle-growing hierarchy	m(ω,8)	m(ω,8)
Hyper-E notation	E2.4082
Hyper-E notation (non-10 base)	\(E[16]2\)
Hyperfactorial array notation	5!	6!
X-Sequence Hyper-Exponential Notation	16{1}2
Steinhaus-Moser Notation	4[3]	5[3]
PlantStar's Debut Notation	[1]	[2]
H* function	H(-0.2)	H(-0.1)
Bashicu matrix system with respect to version 4	(0)[16]	(0)[16]
m(n) map	m(1)(4)	m(1)(5)
s(n) map	\(s(1)(\lambda x . x+1)(127)\)	\(s(1)(\lambda x . x+1)(128)\)

Sources[]

↑ https://www.youtube.com/watch?v=umYvFdU54Po
↑ https://en.wikipedia.org/wiki/Pac-Man#Kill_screen
↑ Cockburn, Alistair. A fuga really big numbers (archived 2016-04-11).
↑ Saibian, Sbiis. The Fz, The Fuga & The Megafuga. Retrieved 2021-07-22.
↑ Cookiefonster. 2.5A. Googological prefixes and suffixes - Pointless Large Number Stuff. Retrieved 2021-07-22.
↑ Part 1 (LAN) - Aarex Googology
↑ https://sites.google.com/view/wlargenumbers/mixed-arrow-notation Retrieved 1/19/2021 6:23 PM EST
↑ BlankEntity's Googology - Celtchar of New World (Retrieved 31 July, 2022)
↑ binary googology stage 1 (retrieved 2024-12-08)
↑ OEIS A002808 - Composite numbers
↑ Wolfram Alpha Is 256 composite?
↑ Wolfram Alpha 256's factors
↑ OEIS A005843 - Even numbers
↑ Wolfram Alpha Is 256 even?
↑ Wolfram Alpha Unhappy Numbers
↑ OEIS A031177 - Unhappy Numbers
↑ OEIS A016754 - Centered octagonal numbers
↑ OEIS A005100 - Deficient numbers

See also[]

Large numbers in computers

Main article: Numbers in computer arithmetic

127 · 128 · 256 · 32767 · 32768 · 65536 · 2147483647 · 4294967296 · 9007199254740991 · 9223372036854775807 · FRACTRAN catalogue numbers
Bignum Bakeoff contestants: pete-3.c · pete-9.c · pete-8.c · harper.c · ioannis.c · chan-2.c · chan-3.c · pete-4.c · chan.c · pete-5.c · pete-6.c · pete-7.c · marxen.c · loader.c
Channel systems: lossy channel system · priority channel system
Concepts: Recursion

Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzthirty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex

Tiaokhiao's circle notation numbers

Mega series: Mega · A-ooga (Megision) · Megisiduon · Megisitruon · Megisiquadruon
Grand Mega series: Grand Mega · Grand Megision · Grand Megisiduon (A-oogra) · Grand Megisitruon · Grand Megisiquadruon
Great Mega series: Great Mega · Great Megision · Great Megisiduon · Great Megisitruon (A-oogrea) · Great Megisiquadruon
Gong Mega series: Gong Mega · Gong Megision · Gong Megisiduon · Gong Megisitruon · Gong Megisiquadruon (A-oogonga)
Hexomega series: Hexomega · Hexomegision · Hexomegisiduon · Hexomegisitruon · Hexomegisiquadruon · Hexomegisiquinton (A-oohexa)
Heptomega series: Heptomega · A-oohepta (Heptomegisisexton) · Octomega · A-oocta · Nonomega · A-ooennea
Megistron series: Megiston (Megistron) · Megisiplextron · Megisiduplextron · Megisitriplextron · Megisiquadruplextron · A-oomega (Megisienneaplextron)
A-ooga series: A-ooga · Betomega (A-oogatiplex) · A-oogatiduplex · A-oogatitriplex · A-oogatiquadruplex · A-oogatiquintiplex
A-oogra series: A-oogra · A-oogratiplex · Betogiga (A-oogratiduplex) · A-oogratitriplex · A-oogratiquadruplex · A-oogratiquintiplex
A-oogrea series: A-oogrea · A-oogreatiplex · A-oogreatiduplex · Betotera (A-oogreatitriplex) · A-oogreatiquadruplex · A-oogreatiquintiplex
A-oogonga series: A-oogonga · A-oogongatiplex · A-oogongatiduplex · A-oogongatitriplex · Betopeta (A-oogongatiquadruplex) · A-oogongatiquintiplex
A-oohexa series: A-oohexa · A-oohexatiplex · A-oohexatiduplex · A-oohexatitriplex · A-oohexatiquadruplex · Betoexa (A-oohexatiquintiplex)
A-oohepta series: A-oohepta · Betozetta (A-ooheptatisextiplex) · A-oocta · Betoyotta · A-ooennea · Betoxota
A-oomega series: A-oomega · A-oomegatiplex · A-oomegatiduplex · A-oomegatitriplex · A-oomegatiquadruplex · Betodaka (A-oomegatienneaplex)
Betomega series: Betomega · Flexinega (Brantomega) · Breatomega · Bigiatomega · Biquadriatomega · Biquintiatomega
Betogiga series: Betogiga · Brantogiga · Flexitria (Breatogiga) · Bigiatogiga · Biquadriatogiga · Biquintiatogiga
Betotera series: Betotera · Brantotera · Breatotera · Flexitera (Bigiatotera) · Biquadriatotera · Biquintiatotera
Betopeta series: Betopeta · Brantopeta · Breatopeta · Bigatopeta · Flexipera (Biquadriatopeta) · Biquintiatopeta
Betoexa series: Betoexa · Brantoexa · Breatoexa · Bigatoexa · Biquadriatoexa · Flexiexa (Biquintiatoexa)
Betozetta series: Betozetta · Flexizetta · Betoyotta · Betoxota · Betodaka
Flexinega series: Flexinega · Oktia (Fainega) · Funnynega · Ftetrinega · Fpentinega · Fhexinega
Flexitria series: Flexitria · Faitria · Oktria (Funnytria) · Ftetritria · Fpentitria · Fhexitria
Flexitera series: Flexitera · Faitera · Funnytera · Oktetra (Ftetritera)
Moser series: Moser · Grand Moser · Great Moser · Gong Moser
Maser series: Maser · Miser (Killaser) · Meser · Muser

Oganso's googology

Penku stage: Two · Four · Nybble · Byte · Short · Int · Long · Overos · Überos · Yfiros · Superos · Hyperos · Ultralos · Hellos · Terolos · Plenolos · Penku

[1] ttps://www.youtube.com/watch?v=umYvFdU54Po

[2] ttps://en.wikipedia.org/wiki/Pac-Man#Kill_screen

[3] Cockburn, Alistair. A fuga really big numbers (archived 2016-04-11).

[4] Saibian, Sbiis. The Fz, The Fuga & The Megafuga. Retrieved 2021-07-22.

[5] Cookiefonster. 2.5A. Googological prefixes and suffixes - Pointless Large Number Stuff. Retrieved 2021-07-22.

[6] Part 1 (LAN) - Aarex Googology

[7] ttps://sites.google.com/view/wlargenumbers/mixed-arrow-notation Retrieved 1/19/2021 6:23 PM EST

[8] BlankEntity's Googology - Celtchar of New World (Retrieved 31 July, 2022)

[9] ry googology stage 1 (retrieved 2024-12-08)

[10] OEIS A002808 - Composite numbers

[11] Wolfram Alpha Is 256 composite?

[12] Wolfram Alpha 256's factors

[13] OEIS A005843 - Even numbers

[14] Wolfram Alpha Is 256 even?

[15] Wolfram Alpha Unhappy Numbers

[16] OEIS A031177 - Unhappy Numbers

[17] OEIS A016754 - Centered octagonal numbers

[18] OEIS A005100 - Deficient numbers

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