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@ -202,52 +202,66 @@ While mathematicians work mostly with infinite number sets and all kinds of "wei
- **symbolic**: Used in some specialized mathematical software to perform symbolic computation, i.e. computation done in a human-like way, by manipulating symbols without using concrete values that would have to resort to approximation.
- ...
However some programming languages, such as [Lisp](lisp.md), sometimes treat numbers in very abstract, more mathematical ways (for the price of some performance loss and added [complexity](bloat.md)) such as exactly handling rational numbers with arbitrary precision, distinguishing between exact and inexact numbers etc.
However some programming languages, such as [Lisp](lisp.md), sometimes treat numbers in very abstract, more mathematical ways (for the price of some performance loss and added [complexity](bloat.md)) such as exactly handling rational numbers with arbitrary precision, distinguishing between exact and inexact numbers etc. The question of number representation is an important one. Though most commonly we meet direct representation, two's complement, floating and fixed point representations, many more alternatives exist that may facilitate storing or manipulation of the values we are to work with. Among these alternatives are for example fractions (numerator and denominator), p-adics, RNS (number stored as its modulo against a fixed set of relatively prime numbers), [BCD](bcd.md) (binary coded decimal digits), factorial base number system and many others.
## Notable Numbers
*See also https://mrob.com/pub/math/numbers.html.*
Here is a table of some numbers and "number like objects" worthy of mention, mostly relevant in math and programming but also some famous ones from [physics](physics.md) and popular [culture](culture.md) (note: the order is roughly from lower numbers to higher ones, however not all of these numbers can be compared easily or at all, so the ordering isn't strictly correct; notes: *&* means base 8, *b3* means base 3).
| number | value | equal to, AKA | notes |
| ----------------------------------- | -------------------- | ---------------------------------------- | ------------------------------------------------------- |
| not a number (NaN, undefined, ...) | none | 1/0, 0^0, tan(pi/2) | error value |
| minus [infinity](infinity.md) | | | not always considered a number, smallest possible value |
| | -1.797693... * 10^308| | smallest number storable in IEEE-754 64 bit float |
| | -3.402823... * 10^38 | | smallest number storable in IEEE-754 32 bit float |
| | -9223372036854776000 | -1 * 2^64 / 2 | minimum two's complement signed 64 bit number |
| | -2147483648 | -1 * 2^32 / 2 | minimum two's complement signed 32 bit number |
| minus thirty two thousand seven ... | -32768 | -1 * 2^16 / 2 | minimum two's complement signed 16 bit number |
| minus one hundred twenty eight | -128 | -1 * 2^7 | minimum value of signed byte (two's complement) |
| minus/negative one | -1 | i^2, j^2, k^2 | |
| minus one twelfth | -0.08333... | -1/12 | by some methods the result of 1 + 2 + 3 + ... |
| minus one twelfth | -0.08333... | -1/12 | infamous, by some methods the result of 1 + 2 + 3 + ... |
| | -3.402823... * 10^38 | | smallest number storable in IEEE-754 32 bit float |
| | -1.797693... * 10^308| | smallest number storable in IEEE-754 64 bit float |
| "[negative zero](negative_zero.md)" | "-0" | 0 | non-mathematical, sometimes used in programming |
| [zero](zero.md) (none, nil) | 0 | "-0", e^(i * pi) + 1, lim x->inf 1/x | "nothing", additive identity |
| epsilon | | 1 / omega | infinitesimal, "infinitely small" non-zero |
| | 4.940656... * 10^-324| | smallest pos. number storable in IEEE-754 64 bit float |
| | 1.401298... * 10^-45 | | smallest pos. number storable in IEEE-754 32 bit float |
| | 1.616255... * 10^-35 | | Planck length in meters, smallest "length" in Universe |
| one hundredth | 0.01 | 1/100, 1%, 0b0.000000101000111101... | |
| | 0.065988... | 1/(e^e) | lowest x such that x^x^x^... is bounded (by 1/e) |
| | 0.071111111111111... | 0x0.123456789abcdef101... | base 16 Champernowne constant |
| one tenth | 0.1 | 1/10, 10%, 0b0.000110011001100111... | |
| | 0.123456789101112... | 0b0.000111111001101011... | base 10 Champernowne constant, normal number |
| one eight | 0.125 | 2^-3, 0b0.001, 0x0.2 | |
| | 0.163264812105216... | &0.1234567101112131415... | base 8 Champernowne constant |
| one fourth | 0.25 | 2^-2, 0b0.01, 0x0.4 | |
| one third | 0.333333... | 3^-1, 0b0.0101010..., ...1313132 (5-adic)| |
| one half | 0.5 | 2^-1, 0b0.1, 0x0.8 | |
| | 0.207879... | i^i, e^(-pi/2) | |
| one fourth | 0.25 | 25%, 2^-2, 1 - 2 + 3 - ..., 0b0.01, 0x0.4| |
| one over pi | 0.318309... | 1/pi, pi^-1 | |
| one third | 0.333333... | 3^-1, ...1313132 (5adic), 1 - 2 + 4 - ...| |
| one over e | 0.367879... | 1/e | optimal solution to the "secretary problem" |
| Thue-Morse constant | 0.412454... | 0b0.011010011001011010... | keep appending negated binary strings (start with 0) |
| prime constant | 0.414682... | 0b0.011010100010100010... | binary number that encodes primes in fractional digits |
| one half | 0.5 | 50%, 2^-1, 0b0.1, 0x0.8 | |
| Euler's constant (gamma) | 0.577215... | 1 + 1/2 + 1/3 + 1/n ... - log(n) | some kinda deep and important constant `O_O` |
| | 0.598958... | base3(0.121011122021221001...) | base 3 Champernowne constant |
| one over square root of two | 0.707106... | 1/sqrt(2), sin(pi/4), cos(pi/4), 2^(-1/2)| |
| | 0.862240124493837... | 0b0.110111001011101111... | base 2 Champernowne constant |
| [one](one.md) | 1 |2^0, 0!, 0.999..., sqrt(1), I, 0b1, cos(0)| NOT a prime, unit, multiplicative identity |
| | 0.123456789101112... | 0b0.000111111001101011... | base 10 Champernowne constant, normal number |
| [square root](sqrt.md) of two | 1.414213... | sqrt(2), 2^(1/2), 0b1.0110101 | irrational, diagonal of unit square, important in geom. |
| ten over seven | 1.428571... | 10/7 | common approximation of sqrt(2) |
| supergolden ratio | 1.465571... | solve(x^3 - x^2 - 1 = 0) | similar to golden ratio, bit more difficult to compute |
| Euler's constant | 0.577215... | 1 + 1/2 + 1/3 + 1/n ... - log(n) | some kinda deep and important constant `O_O` |
|phi ([golden ratio](golden_ratio.md))| 1.618033... | (1 + sqrt(5)) / 2, solve(x^2 - x - 1 = 0)| irrational, visually pleasant ratio, divine proportion |
| square root of three | 1.732050... | sqrt(3), 3^(1/2), 0b1.1011101 | irrational |
| square root of pi | 1.772453... | sqrt(pi) | |
| [two](two.md) (couple, pair) | 2 | 2^1, 2!, 2!!, 0b000010, II, 0b10 | (only even) prime, base of [binary](binary.md) system |
| [silver ratio](silver_ratio.md) | 2.414213... | 1 + sqrt(2), solve(x^2 - 2 * x - 1 = 0) | similar to golden ratio |
| nineteen over seven | 2.714285... | 19/7 | common approximation of e |
| [e](e.md) (Euler's number) | 2.718281... | 0b10.1011011 | base of natural [logarithm](log.md) |
| [three](three.md) | 3 | 2^2 - 1, III, Ob11, 2^1.584... | prime, max. number on 2 bits, regular plane tilings |
| [pi](pi.md) | 3.141592... | 2 * asin(1), 0b11.0010010 | circle circumference to its diameter, irrational |
| twenty two over seven | 3.142857... | 22/7 | common approximation of pi |
| square root of ten | 3.162277... | sqrt(10) | approximation of pi |
| [four](four.md) | 4 | 2^2, 0b000100, IV, 0b100 |first composite number, min. needed to color planar graph|
| [five](five.md) | 5 | 3^2 - 2^2, V, 0b101, fib(5) | (twin, triplet) prime, number of platonic solids, Fib. |
| [six](six.md) (half dozen) | 6 | 3!, 1 * 2 * 3, 1 + 2 + 3, VI, 0b110 | highly composite number, 1st perfect number |
@ -255,85 +269,109 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| [thrembo](thrembo.md) | ??? | | the hidden number |
| [seven](seven.md) | 7 | 2^3 - 1, VII, &7, 0b111 |(twin) prime, days in week, max. unsigned n. with 3 bits |
| [eight](eight.md) | 8 | 2^3, 0b001000, VIII, &10, 0b1000, fib(6) | base of [octal](oct.md) system, 7th Fibonacci number |
| [nine](nine.md) | 9 | 3^3, 1^3 + 2^3, sqrt(81), IX, 0b1001 | |
| | 8.539734... | pi * e | |
| [nine](nine.md) | 9 | 3^2, 1^3 + 2^3, sqrt(81), IX, 0b1001 | |
| pi squared | 9.869604... | pi^2 | |
| [ten](ten.md) | 10 |10^1, 1 + 2 + 3 + 4, X, 0b1010, 2^3.321...| your IQ? :D base of our decimal system |
| eleven | 11 | 0xb, b3(102), &13, 0b1011, XI | palindromic twin prime |
| twelve (dozen) | 12 | 2 * 2 * 3, 0xc, 0b1100, XII | highly composite number |
| thirteen (long or devil's dozen) | 13 | fib(7), 0xd, 0b1101, XIII | prime considered unlucky (in west and China), Fib. num. |
| thirteen (long or devil's dozen) | 13 | fib(7), trib(7), 0xd, 0b1101, XIII | prime considered unlucky (in west and China), Fib. num. |
| fourteen | 14 | &112, 0b1110, 0xe, XIV | |
| fifteen | 15 | 2^4 - 1, 0b1111, 0xf, 1 + 2 + 3 + 4 + 5 | maximum unsigned number storable with 4 bits |
| [sixteen](sixteen.md) | 16 | 2^4, 4^2, 2^2^2, 0b010000, &20, 0x10, XVI| base of [hexadecimal](hex.md) system |
| seventeen | 17 | 0b10001, &21, 0x11, XVII | twin&sexy prime, binary palindrome |
| eighteen | 18 | 0b10010, &22, 0x12, XVIII | |
| nineteen | 19 | 0b10011, &23, 0x13, XIX | twin&sexy prime |
| twenty | 20 | 0b10100, &24, 0x14, XX | |
| twenty | 20 | 0b10100, &24, 0x14, XX, score | largest number of faces for a Platonic solid |
| twenty one | 21 | 0b10101, 0x15, BB(3), fib(8), 0x15, XXI | maximum number of 1s produced by 3 state Turing Machine |
| twenty three | 23 | 0b10111, &27, 0x17, | sexy prime |
| twenty four | 24 | 2 * 2 * 2 * 3, 4!, 0x18, XXIV |highly composite number, possible ways to order 4 objects|
| twenty three | 23 | 0b10111, &27, 0x17, XXIII | sexy prime |
| twenty four | 24 | 2 * 2 * 2 * 3, 4!, trib(8), 0x18, XXIV |highly composite number, possible ways to order 4 objects|
| twenty five | 25 | 5^2, sqrt(625), 0x19, XXV | |
| twenty seven | 27 | 3^3, 0b11011, 0x1b, &33, 0x1b, XXVII | palindrome in base 2 and 8 |
| twenty eight | 28 | 0b11100, 0x1c, XXVIII | 2nd perfect number |
| twenty nine | 29 | 0b11101, &1002, 0x1d, XXIX | twin&sexy prime |
| thirty | 30 | 0b11110, &1010, 0x1e, XXX | |
| thirty one | 31 | 2^5 - 1, 0b11111, &37, 0x1f, XXXI |max. unsigned number storable with 5 bits, Mersenne prime|
| [thirty two](thirty_two.md) | 32 | 2^5, 0b100000, &40, 0x20, XXXII | number of possible values storable with 5 bits |
| thirty three | 33 | 1! + 2! + 3! + 4!, XXXIII | |
| thirty four | 34 | fib(9), 0x22, XXXIV | Fibonacci number |
| thirty six | 36 | 2 * 2 * 3 * 3, XXXVI | highly composite number |
| thirty seven | 37 | 0b100101, 0x25, XXXVII | most commonly picked 1 to 100 "random", permutable prime|
| forty | 40 | 0b101000, 0x28, XL | |
| forty one | 41 | 0b101001, 0x29, XLI | twin&sexy prime |
| [forty two](42.md) | 42 | XLII | cringe number, answer to some stuff, unlucky in Japan |
| forty three | 43 | 0b101011, 0x2b, XLIII | twin&sexy prime |
| forty three | 43 | 0b101011, 0x2b, XLIII | twin&sexy prime, 4th Sylvester's number |
| forty four | 44 | trib(9), 0b101100, 0x2c, XLIV | Tribonacci number |
| forty seven | 47 | 0b101111, 0x2f, XLVII | sexy prime |
| forty eight | 48 |2^5 + 2^4, 2 * 2 * 2 * 2 * 3, XLVIII, 0x30| highly composite number |
| forty nine | 49 | 7^2 | |
| fifty | 50 | L | |
| forty nine | 49 | 7^2, XLIX | |
| fifty | 50 | 0x32, L | |
| fifty three | 53 | 0b110101, 0x35, LIII | sexy prime |
| fifty five | 55 | fib(10), 1 + 2 + ... + 10, LV | sum of numbers up to 10, 11th Fibonacci number |
| fifty nine | 59 | 0b111011, 0x3b, LIX | twin&sexy prime |
| sixty | 60 | 0x3c, LX | highly composite number, used in time measuring |
| sixty | 60 | 2^2 * 3 * 5, 0x3c, LX, threescore | (super.) highly composite number, used in time measuring|
| sixty one | 61 | 0x3d, LXI | twin&sexy prime |
| sixty three | 63 | 2^6 - 1, 0b111111, &77, 0x3f, LXIII | maximum unsigned number storable with 6 bits |
| [sixty four](sixty_four.md) | 64 | 2^6, 0b1000000, &100, 0x40, LXIV | number of squares on a chess board |
| sixty seven | 67 | 0x43, LXVII | sexy prime |
| [sixty nine](69.md) | 69 | 0x45, LXIX | sexual position |
| seventy | 70 | 0x46, LXX | |
| seventy one | 71 | 0x47, LXXI | twin prime |
| seventy three | 73 | 0b1001001, 0x49, LXXIII | twin&sexy prime, binary palindrome |
| seventy five | 75 | 0x5b, LXXV | |
| seventy nine | 79 | 0x4f, LXXIX | sexy prime |
| eighty one | 81 | 3^4, 9*9, XXCI | |
| eighty | 80 | 0x50, LXXX | |
| eighty one | 81 | trib(10), 3^4, 9^2, XXCI | Tribonacci number |
| eighty three | 83 | LXXXIII | sexy prime |
| eighty eight | 88 | 0x58, LXXXVIII | number of essentially different cellular automata |
| eighty nine | 89 | fib(11), 0x59, LXXXIX | Fibonacci number, sexy prime |
| ninety six | 96 | 2^5 + 2^6, 5! - 4!, 0x60 | alternative sexual position |
| ninety | 90 | 0x5a, XC | |
| ninety six | 96 | 2^5 + 2^6, 5! - 4!, 0x60, XCVI | alternative sexual position |
| ninety seven | 97 | XCVII | sexy prime |
| ninety nine | 99 | 10^2 - 1, 0b1100011 | palindrome in base 2 and 10 |
| one hundred | 100 | 10^2, 0x64, C, 2^6.643... | |
| one hundred seven | 107 | BB(4), CVII | maximum number of 1s produced by 4 state Turing machine |
| one hundred twenty | 120 | 5!, C(10,3), CXX | possible ways to order 5 objects, highly composite |
| one hundred eight | 108 | 0x6c, CVIII, 1 * 2^2 * 3^3, hyperfact(3) | |
| one hundred twenty | 120 | 2^3 * 3 * 5, 5!, C(10,3), CXX | possible ways to order 5 objects, highly composite |
| one hundred twenty one | 121 | 11^2, CXXI | [palindromic](palindrome.md) |
| one hundred twenty five | 125 | 5^3, CXXV | |
| one hundred twenty seven | 127 | 2^7 - 1, 0b01111111, &177, 0x7f, CXXVII | maximum value of signed byte, Mersenne prime |
| one hundred twenty seven | 127 | 2^7 - 1, 0b01111111, &177, 0x7f, CXXVII | maximum value of signed byte, 4th Mersenne prime |
| one hundred twenty eight | 128 | 2^7, 0x80, &200, CXXVIII, 10^2.107... | number of values storable with 7 bits |
| one hundred forty four (gross) | 144 | 12^2, fib(12), CXLIV | 13th Fibonacci number, 12 dozen |
| one hundred fifty | 150 | 0x96, CL | |
| one hundred sixty eight | 168 | 24 * 7, CLXVIII | hours in week |
| one hundred eighty | 180 | 2^2 * 3^2 * 5, 0xb4, CLXXX | highly composite, degrees in half of full angle |
| two hundred | 200 | 0xc8, CC | |
| twi hundred forty | 240 | 0xf0, CCXL | highly composite |
| two hundred forty three | 243 | 3^5, 0xf3, CCXLIII | |
| two hundred fifty five | 255 | 2^8 - 1, 0b11111111, &377, 0xff, CCLV |maximum value of unsigned [byte](byte.md), hex palindrome|
| two hundred fifty six | 256 | 2^8, 4^4, 16^2, 0x100, ((2^2)^2)^2, CCLVI| number of values that can be stored in one byte |
| two hundred eighty eight | 288 | 0x120, CCLXXXVIII, 1^1 + 2^2 + 3^3 + 4^4 | |
| three hundred | 300 | 0x12c, CCC | |
| three hundred forty three | 343 | 7^3, CCCXLIII | palindrome |
| three hundred sixty | 360 | 2 * 2 * 2 * 3 * 3 * 5, CCCLX | highly composite number, degrees in full circle |
| three hundred sixty five | 365 | 0x16d, CCCLXV | days in a year, binary palindrome |
| four hundred | 400 | 0x190, CD | |
| four hundred twenty | 420 | 0x1a4, CDXX | stoner shit (they smoke it at 4:20), divisible by 1 to 7|
| four hundred ninety six | 496 | 0x1f0, CDXCVI | 3rd perfect number |
| five hundred | 500 | 0x1f4, D | |
| five hundred eleven | 511 | 2^9 - 1, DXI | largest number storable with 9 bits |
| five hundred twelve | 512 | 2^9, 2^(3^2), DXII | number of values storable with 9 bits |
| six hundred twenty five | 625 | 25^2, 5^4, DCXXV | |
| six hundred and sixty six | 666 | 0x29a, DCLXVI | number of the beast, palindromic |
| seven hundred twenty | 720 | 6!, 3!!, DCCXX | possible ways to order 6 objects, highly composite |
| seven hundred twenty | 720 | 2^4 * 3^2 * 5, 6!, 3!!, DCCXX | possible ways to order 6 objects, highly composite |
| seven hundred twenty nine | 729 | 3^6, (3^2)^3, DCCXXIX | |
| shitload | ??? | a lot | expressed a bigger quantity |
| one thousand (grand) | 1000 | 10^3, M, 0x3e8, 2^9.965... | |
| seven hundred fifty | 750 | 0x2ee, DCCL | |
| shitload | ??? | clusterfuck, a lot | expressed a bigger quantity |
| nine hundred ninety nine | 999 | 10^3 - 1, 0x3e7, CVXCIX | palindromic |
| one thousand (grand) | 1000 | 1K, 10^3, M, 0x3e8, 2^9.965... | |
| one thousand twenty three | 1023 | 2^10 - 1, &1777, 0x3ff, MXXIII | largest number storable with 10 bits |
| one thousand twenty four | 1024 |2^10, 4^5, &2000, 0x400, MXXIV, 10^3.01...| number of values storable with 10 bits |
| one thousand three hundred ... | 1337 | 0x539, MCCCXXXVII | [leet](leet.md) number |
| one thousand six hundred eighty | 1680 | 0x690, MDCLXXX | highly composite, often used as horizontal resolution |
| one thousand seven hundred ... | 1729 | 0x6c1, MDCCXXIX | Ramanujan number, taxican number, part of math lore |
| one thousand eight hundred ... | 1807 | 0x70f, MDCCCVII | 5th Sylvester's number |
| two thousand | 2000 | 0x7d0, MM | |
| two thousand forty eight | 2048 | 2^11, 0x800, MMXLVIII | number of values storable with 11 bits |
|two thousand one hundred eighty seven| 2187 | 3^7, 0x88b, MMCLXXXVII | |
| two thousand four hundred one | 2401 | 7^4, MMCDI | |
@ -341,16 +379,23 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| three thousand nine hundred ... | 3999 | MMMCMXCIX | largest number that can be written with Roman numerals |
| four thousand ninety five | 4095 | 2^12 - 1, &7777, 0xfff | maximum unsigned integer storable with 12 bits |
| four thousand ninety six | 4096 | 2^12, 2^(3^4), &10000, 0x1000 | number of values storable with 12 bits |
| five thousand | 5000 | 0x1388 | |
| five thousand forty | 5040 | 7!, 1 * 2 * ... * 7 | possible ways to order 7 objects |
| five thousand fifty | 5050 | 1 + 2 + ... + 100 | sum of numbers up to 100 |
| six thousand five hundred sixty one | 6561 | 3^8, 3^(2^3) | |
|six thousand seven hundred sixty five| 6765 | fib(20), 0x1a6d | Fibonacci number |
|eight thousand one hundred ... | 8128 | 0x1fc0 | 4th perfect number |
| seven thousand seven hundred ... | 7734 | 0x1e36 | on a calculator say "hello" (upside down) |
| eight thousand one hundred ... | 8128 | 0x1fc0 | 4th perfect number |
|eight thousand one hundred ninety one| 8191 | 0x1fff, 2^13 - 1 | 5th Mersenne prime |
|eight thousand one hundred ninety two| 8192 | 0x2000, 2^13 | number of values storable with 13 bits |
| ten thousand (myriad) | 10000 | 10^4, 100^2, 2^13.287... | |
| fifteen thousand six hundred ... | 15625 | 5^6, 0x3d09 | |
| sixteen thousand three hundred ... | 16384 | 2^14, 0x4000 | number of values storable with 14 bits |
| sixteen thousand eight hundred ... | 16807 | 7^5, 0x41a7 | |
| nineteen thousand six hundred ... | 19683 | 3^9, 3^(3^3), 0x4ce3 | |
|twenty seven thousand six hundred ...| 27648 | 1 * 2^2 * 3^3 * 4^4, hyperfact(4) | |
|thirty two thousand seven hundred ...| 32767 | 2^16 / 2 - 1, 0x7fff | maximum two's complement signed 16 bit number |
|thirty two thousand seven hundred ...| 32768 | 2^15, 0x8000 | number of values storable with 15 bits |
| forty thousand three hundred twenty | 40320 | 8!, 1 * 2 * ... * 8, 0x9d80 | possible ways to order 8 objects |
| ... (enough lol) | 59049 | 3^10, 0xe6a9 | |
| | 65504 | | largest number storable in IEEE-754 16 bit float |
@ -360,10 +405,12 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| | 80085 | | looks like BOOBS |
| | 86400 | 60 * 60 * 24 | seconds in a day |
| hundred thousand | 100000 | 10^5, 2^16.609... | |
| | 131071 | 2^17 - 1 | 6th Mersenne prime |
| | 362880 | 9!, 1 * 2 * ... * 9 | possible ways to order 9 objects |
| | 500500 | 1 + 2 + ... + 1000 | sum of numbers up to 1000 |
| one [million](million.md) | 1000000 | 10^6, 0xf4240, 2^19.931... | |
| one [million](million.md) | 1000000 | 1M, 10^6, 0xf4240, 2^19.931... | |
| | 3197281 | | number of possible chess games after 4 half moves |
| | 3263443 | | twin prime, 6th Sylvester's number |
| | 3628800 | 10!, 1 * 2 * ... * 10 | possible ways to order 10 objects |
| | 16777216 | 2^24, 16^6, 0xffffff | number of distinct 24 bit values, no. of RGB24 colors |
| | 16777217 | 2^24 + 1, 0x1000000 | min. pos. int. unstorable in 32b float (prec. falls < 1)|
@ -372,9 +419,10 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| | 31556926 | | seconds in a year |
| | 33550336 | | 5th perfect number |
| | 39916800 | 11!, 1 * 2 * ... * 11 | possible ways to order 11 objects |
| | 86400000 | 1 * 2^2 * 3^3 * 4^4 * 5^5, hyperfact(5) | |
| | 479001600 | 12!, 1 * 2 * ... * 12 | possible ways to order 12 objects |
| one [billion](billion.md) | 1000000000 | 10^9, milliard, 0x3b9aca00, 2^29.897... | |
| | 2147483647 | 2^32 / 2 - 1 | maximum two's complement signed 32 bit number |
| one [billion](billion.md) | 1000000000 |1B, 10^9, milliard, 0x3b9aca00, 2^29.89...| |
| | 2147483647 | 2^32 / 2 - 1 |maximum two's complement signed 32 bit number, Mer. prime|
| | 3735928559 | 0xdeadbeef | one of famous hexadeciaml constants, spells out DEADBEEF|
| | 4294967295 | 2^32 - 1, 0xffffffff | maximum unsigned number storable with 32 bits |
| | 4294967296 | 2^32, ((((2^2)^2)^2)^2)^2, 0x100000000 | number of values storable with 32 bits |
@ -382,10 +430,13 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| | 8589869056 | 0x1ffff0000 | 6th perfect number |
| | 9876543210 | 0x24cb016ea | all decimal digits from highest to lowest |
| | 87178291200 | 14!, 1 * 2 * ... * 14 | possible ways to order 14 objects |
| hundred billion | 100000000000 | 10^11 | approximate number or stars in Milky Way galaxy |
| | 137438691328 | 0x1ffffc0000 | 7th perfect number |
| | 500000500000 | 1 + 2 + ... + 1000000 | sum of numbers up to 1000000 |
| one trillion | 1000000000000 | 10^12, billion (LS) | |
| | 1307674368000 | 15! | possible ways to order 15 objects |
| | 4031078400000 | 2^2 * 3^3 * 4^4 * 5^5 * 6^6, hyperfact(6)| |
| | 10650056950807 | | 7th Sylvester's number |
| | 20922789888000 | 16! | possible ways to order 16 objects |
| thirty trillion | 30000000000000 | | approximate number of cells in human body |
| | 355687428096000 | 17! | possible ways to order 17 objects |
@ -411,6 +462,7 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| | 3.402823... * 10^38 | 2^128 | number of values storable with 128 bits |
| | 1.915619... * 10^53 | | 10th perfect number |
| | 1.157920... * 10^77 | 2^256 | number of values storable with 256 bits |
| bazillionplex | ??????? | 10^bazillion | one followed by bazillion zeros |
| | 10^80 | | approx. number of atoms in observable universe |
| [googol](googol.md) | 10^100 | | often used big number |
| Shannon number | 10^120 | | estimated number of possible games in [chess](chess.md) |
@ -421,8 +473,10 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| | 1.797693... * 10^308 | | largest number storable in IEEE-754 64 bit float |
| | 1.797693... * 10^308 | 2^1024 | number of values storable with 1024 bits |
| | 3.231700... * 10^616 | 2^2048 | number of values storable with 2048 bits |
| | 2.601218... * 10^1746| 3!!! | |
| | 4.023872... * 10^2567| 1000! | possibe ways to order 1000 objects |
| [googolplex](googolplex.md) | 10^(10^100) | 10^googol | another large number, number of genders in 21st century |
| | 10^^10 | 9PT10, 10^10^10^10^10^10^10^10^10^10 | |
| [Graham's number](grahams_number.md)| | g64 | extremely, unimaginably large number, > googolplex |
| TREE(3) | unknown | | yet even larger number, > Graham's number |
| [infinity](infinity.md) | | lim x->0 1/x, 1 + 1 + 1 + ... | not always considered a number, largest possible value |
@ -430,6 +484,8 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
| [i](i.md) (imaginary unit) | | j * k | part of complex numbers and quaternions |
| [j](j.md) | | k * i | one of quaternion units |
| [k](k.md) | | i * j | one of quaternion units |
| 1/sqrt(2) + i/sqrt(2) | | sqrt(i) | one of the square roots of imaginary unit |
| -1/sqrt(2) - i/sqrt(2) | | sqrt(i) | one of the square roots of imaginary unit |
## See Also