ou

largest negative integer

value assigned to the divergent infinite series

zero

cardinality of the empty set

the additive identity

was represented using a shell in the ancient Mayan civilisation

real part of all non-trivial zeros of the Riemann zeta function – if the Riemann hypothesis is true!

Euler–Mascheroni constant *γ*

the limiting difference between the harmonic series and the natural logarithm

Catalan’s constant *G*

the result of the infinite series

unknown whether irrational or not

the multiplicative identity

the only natural number that isn’t prime or composite

wasn’t considered a “number” by many ancient and medieval mathematicians

proportion between the frequencies of adjacent semitones in the 12 tone equal temperament scale

Apéry’s constant

sum of the reciprocals of the positive cubes:

appears in quantum electrodynamics and random spanning trees

can’t be constructed using ruler a compass, which was one of the three famous geometric problems of antiquity

first known irrational number, discovered by Pythagoras or one of his students

ratio of diagonal and the side length in a square

proportion between the sides of DIN paper sizes

Golden ratio *φ*

the larger of the two real roots of

ratio of the side and one of the diagonals in a pentagon

the measure of the fish

length of the space diagonal of a cube with edge length 1

height of an equilateral triangle with side length 2

smallest and only even prime number

Euler characteristic of a polyhedron homeomorphic to a sphere

length of the diagonal of a 1 × 2 rectangle

second Feigenbaum constant *α*

ratio between the width of a tine and the width of one of its two subtines

Euler’s number *e*

limit of *n* approaches infinity

unique positive number *a* such that the graph of the function

number of dimensions we can see

number of particles generations in the standard model

first Mersenne prime

Pi or *π*

circumference of a circle with diameter 1

transcendental number, which means that the famous ancient problem of squaring a circle is impossible

closely approximated by

smallest composite number

maximum number of colours needed to colour any map in the Euclidean plane

number of Nucleobase types in the DNA: A, G, C, T

unlucky number in Chinese, Japanese and Korean culture

first Feigenbaum constant *δ*

limiting ratio of consecutive bifurcation intervals in a one-parameter logistic map

number of Platonic solids

number of vertices of a pyramid

number of vertices in the smallest non-planar (K5)

the cycle of fifths underlies to musical harmonies

fifth Fibonacci number

smallest perfect number

order of the smallest non-abelian group

number of distinct Quarks

number of regular polytopes

Tau

circumference of a circle with radius 1

period of the sin, cos and tan functions

number of vertices of the smallest polygon that can’t be constructed with ruler and compass

number of hills in Rome and wonders of the ancient world

secret agent number of James Bond

number of days in a week

largest Fibonacci Number which is a cube

order of the smallest non-commutative unitary ring

number of tentacles of an octopus

number of bits in a byte

lucky number in Chinese culture: its name sounds similar to “prosperity”

maximum number of cubes needed to sum to any positive integer

number of muses in Greek mythology

exponential factorial, since

number of significant points in a triangle that lie on a circle: the Nine-Point circle

base of our number system

house number of the British Prime Minister

number of Jewish and Christian commandments

sum of the first three primes, first four integers and first four factorials

smallest palindrome in base-10

number of space-time dimensions in M-theory

first Apollo mission to land of the moon

number of players in a football team

only sublime number less than 1 trillion

smallest abundant number

number of months per year and signs in the Zodiac

number of faces of the dodecahedron

number of different Archimedean solids

number of cards of a suit

unlucky number in Western culture

sum of the first three squares, i.e. a square-pyramidal number

open meandric number: the number of meanders in non-self-intersecting oriented curves

number of pounds in one stone

fourth Catalan number

magic constant in a 3×3 magic square.

largest composite number with one one group of that order

triangular, hexagonal, pentatope and Bell number

only number of the form *x* and *y* distinct integers

number of pawns in a chess set, and each player starts with 16 pieces

length of credit card numbers

number of wallpaper groups

“least random number” or Feller Number

sum of the first 4 prime numbers, and only prime which is the some of 4 consecutive primes

only non-zero number that is twice the sum of its digits.

sum of the first three pentagonal numbers, making it a “pentagonal pyramidal number”

lucky number and the value for life in Jewish numerology

maximum number of 4th powers needed to sum to any number

number of cells in the only non-trivial magic hexagon

number of rooted trees with 6 vertices

number of faces of an icosahedorn and vertices of a dodecahedron

number of quarter or half turns required to optimally solve a Rubik’s cube in the worst case

base of the ancient Mayan number system

sum of the first 4 triangular numbers, and thus a tetrahedral number

magic number in Blackjack

number of dots on a 6-sided die

smallest number of distinct squares into which a square can be dissected

smallest Fibonacci number whose digits and digit sums are also Fibonacci

number of partitions of 8

number of Major Arcana cards in divinatory Tarot

pentagonal and a centred heptagonal number

least number of distinct integer-sided cuboids needed to make up another cuboid

number of unsolved problems posed by Hilbert in 1900

smallest odd non-twin prime

number of people required so that the probability of a shared birthday is greater than 50%

Gelfond’s constant

largest number divisible by all integers less than its square root

only non-trivial integer

number of hours in a day

smallest square that can be written as a sum of two squares.

automorphic, aspiring and non-sociable number

number of sporadic groups

only positive number to be directly between a square and a cube

smallest non-palindromic number whose square is a palindrome:

sum of the digits of its cube:

in the Collaz Conjecture you need 112 steps to get from 27 to 1

second perfect number

harmonic divisor number, happy number and triangular number

number of days in the lunar cycle

number of dominoes in a standard double-six set

largest Prime that is the sum of three consecutive square numbers: 4 + 9 + 16 = 29

Saturn requires over 29 years to orbit the Sun

sum of the first four squares

largest number such that all smaller numbers coprime to it are prime

number of edges of the icosahedron and dodecahedron

smallest sphenic number

centered triangular, pentagonal and decagonal number

Mersenne, lucky and supersingular prime

number of musical triads (12 major, 12 minor, 4 diminished, and 3 augmented)

most common number of days per month

11111 in base 2

ninth happy number

smallest nontrivial fifth power

sum of the totient functions of the first ten integers

freezing point of water at sea level in Fahrenheit

largest integer that isn’t the sum of distinct triangular numbers

number of vertebrae in a human spine

sum of the first four factorials

smallest number that has the same number of divisors as the previous and following number

magic number of the order four magic square

nontotient and noncototient number

number of different hexominoes

sum of the first five triangular numbers

highly cototient and tetrahedral number

smallest non-trivial number which is both square and triangular

sum of the cubes of the first three integers.

the sum of the first 36 integers is 666

maximum number of 5th powers needed to sum to any number

lucky, irregular, unique and cuban prime

human body temperature in degrees Celsius

number of plays written by Shakespeare

magic number of an order 3 magic hexagon

number of slots in American Roulette

largest even number which cannot be written as the sum of two odd composite numbers

sum of five consecutive primes: 3 + 5 + 7 + 11 + 13

sum the first three powers of three: 3 + 9 + 27

number of steps in the title of a Hitchcock film

only number whose letters are in alphabetical order

Venus returns to the same point in the night sky every 40 years

octagonal number

number of days in Lent

the polynomial

lucky number of Euler, and the largest such prime

number of Mozart’s last symphony

answer to the Ultimate Question of Life, the Universe, and Everything, according to Deep Thought

magic number in a 3×3×3 magic cube

fifth Catalan number

Lowest atomic number of any element without stable isotopes

smallest prime that is not a Chen prime

smallest prime number expressible as the sum of two, three, four or five primes

number of derangements of 5 items

largest number of regions the plane can be divided into by 7 circles

Tribonacci, happy and octahedral number

third Kaprekar number, since

triangular, hexagonal and 16-gonal number

number of human Chromosomes

Erdős–Woods number

Wedderburn-Etherington number

largest number of cubes that cannot tile a cube

atomic number of silver

not a palindrome in any base *b* for

Carol number

double factorial of 6

number of Ptolemaic tessellations

highly composite number and the smallest number with 10 divisors

multiplying the period of

type

smallest number that can be written as the sum of of two squares in two distinct ways:

represented by the letter L in Roman numerals

number of ways to draw non-intersecting lines between six points on the boundary of a circle

both a pentagonal number and a centred pentagonal number

number of a highly classified United States Air Force facility

number of playing cards in a standard deck (4 suits with 13 cards each)

number of white keys on a piano

untouchable number, because it is never the sum of the proper divisors of any other number

can be written as 35 (reversed) in hexadecimal, a property shared by many multiples of 53

smallest prime number that does not divide the order of any sporadic group

number of coloured squares on a Rubik’s cube

perfect round on a par 72 golf course

largest number that is both triangular and Fibonacci

sum of the first 10 integers

square pyramidal number, since it is the sum of the first 5 square numbers

maximum determinant of an 8*8 matrix of zeroes and ones

sum of the first six triangular numbers or the first six odd primes

tetranacci and pronic number

can be written as 111 in base 7

Leyland number, since

the 57-cell is a self-dual abstract regular four-dimensional polytope.

number of degrees in 1 radian

number of commutative semigroups of order 4

sum of the first seven Prime numbers

number of stellations of an icosahedron

number of orthorhombic space groups

order of the smallest non-abelian simple group

base of the Babylonian number system

number of minutes in one hour and one degree

appears three times in the list of Fortunate numbers

maybe the largest prime dividing the product of the next two primes plus 1

only number whose cube, 238328, consists of three digits each occurring two times

written as 222 in base 5

number of partially ordered sets of 5 elements

number of tiles on a chess board

superperfect number with

maximum number of strokes in any Chinese character

smallest number with 7 divisors

index of Graham’s number in the sequence 3, 27, 7625597484987, …

smallest number that becomes a square when its reverse is either added to or subtracted from it

sum of the first 22 integers

largest number below 2000 not containing an ‘e’ (an eban number)

smallest number that is palindromic in bases 5 and 6

maximal number of letters in website domains

irregular and lucky and Pillai prime

truncated Tetrahedral Number

number of tetragonal space groups

in a normal distribution, 68% of values are within one standard deviation of the mean

its square and its cube together contain every digit exactly once

largest factorial on many calculators

smallest weird number: an abundant number which is not the sum of any subset of its divisors

a Pell number and a generalised heptagonal number

algebraic degree of Conway’s constant

divides the sum of all primes less than it

largest prime factor of the order of any sporadic simple group

maximum number of spheres that can touch each other in a lattice packing in 6 dimensions

average number of heartbeats per minute

smallest Achilles number

least number of sixths powers needed to sum to every integer

the 21st prime number and its reverse, 37, is the 12th prime number

number of non-Hamiltonian polyhedra with a minimum number of vertices

number of uniform polyhedra, excluding the infinite set

pentagonal pyramidal number

atomic number of the densest element, Osmium

number of books in the Catholic bible

largest integer that cannot be written as a sum of distinct numbers whose reciprocals sum to 1

maximum number of given digits in a sudoku puzzle, for it to lack a unique solution.

smallest integer that can be written as the sum of four distinct squares in three ways

atomic number of Gold.

fortunate, Gaussian, happy, Higgs, Kynea, lucky, permutable, Pillai and regular prime

days needed by Phileas Fogg to travel around the world

number of columns in IBM punch cards

number of stable chemical elements

only non-trivial number which is the square of the sum of its digits

its inverse

sixth nuclear magic number

humber of 6-hexes, shapes made by joining six regular hexagons

atomic number of Bismuth, the heaviest stable element

Sophie Germain and Eisenstein prime

number of 5-faces of a seven-dimensional hypercube

largest order of a permutation of 14 elements

centered triangular, square, 14-gonal and 8-gonal number

number of ways to tie a tie

can be written as 222 in base 6

number of metals in the periodic table

happy number

sum of the squares of the first four primes

sum of the divisors of the first ten integers

only number known whose square has no isolated digits.

numbers of keys on a piano.

numbers of constellations in the sky

number of days in a year on Mercury

equals

11th Fibonacci number

number of degrees in a right angle

number of edges of a truncated Icosahedron

unitary perfect number and Pronic number

latitude of the North and South poles

smallest non-trivial cabtaxi number

sum of the squares of the first six integers.

smallest pseudoprime satisfying

number of faces of the snub dodecahedron

highest number of faces of any Archimedean solid

number of “atomic elements” in the Look-and-say sequence

atomic number of Uranium.

can be written as 333 in base 5

Mertens function returns 0 for 93

sum of the integers from 13 to 18

number of sets with 8 integers so that each is a proper divisor of the product of the others plus 1

number of graphic non-whitespace characters in ASCII

smith number, since the sum of its digits equals the sum of its prime factors

94! – 1 is prime

smallest non-interesting number

untouchable number, since it cannot be expressed as the sum of some of the proper divisors of another integer

the decimal expansion of its reciprocal starts with the powers of two:

boiling point of water in Celsius

denoted by the letter C in Roman numerals

sum of the first four cubes:

number of heptominoes (one of which contains a whole)

sacred number in the Dharmic Religions

magic constant of the smallest magic square composed only of prime numbers and 1

magic constant of a 6×6 magic square

A113 was the Pixar animation classroom at the California Institute of the Arts

smallest number which can be written as the sum of three integers in four different ways, so that the product of every triple is the same: 118 = 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72

smallest number that is the product of 7 prime factors (

largest number that is not the sum of distinct squares

power of 2, all of whose digits are powers of 2 (unknown if there are any other numbers with this property)

smallest number that is the sum of all 2-digit numbers made from its digits

sixth Catalan number

one of just four numbers to be the sum of the factorials of its digits: 145 = 1! + 4! + 5!

sum of the cubes of its integers:

sum of the first 5 factorials and the first 17 natural numbers

the boiling point of water in Fahrenheit

largest number that can be represented using an 8-bit unsigned integer

smallest base 2 Fermat pseudoprime

average number of days in a year, consisting of 365 days, 5 hours 48 minutes and 46.08 seconds

number of octominoes

the A380 is the world’s largest passenger aircraft.

third perfect number

denoted by the letter D in Roman numerals

number of the beast

smallest palindromic square whose square root 26 is not palindromic

equals 6!

can be written as the product of consecutive integers in two different ways: 720 = 10 × 9 × 8 = 6 × 5 × 4 × 3 × 2

the Boeing 747 aircraft is called the “Queen of the Skies”

sacred number in Muslim Abjad numerology

second weird number, after 70

equals

is the product of three consecutive primes 7 × 11 × 13

1089 × 9 = 9801, the reverse of its digits

the result if you take any 3-digit number, subtract its reversal, and the difference to its own reversal (for example,

title of George Lucas’ first film: THX 1138

number of 9-ominoes

one of just 5 numbers that is both triangular and tetrahedral

Hardy–Ramanujan number and second taxicab number

smallest positive integer that can be written as the sum of two positive cubes in two different ways:

current year

number of pounds in an (English) ton

smallest number with 5 different prime factors, since

equals

smallest number to appear 8 times in Pascal’s triangle (there is no other number less than 2^23 appearing 8 times)

Munchausen Number: a number that is the sum of each digit raised to itself. The only non-trivial example is

number of seconds in one hour

largest number that can be written in Roman numerals, as MMMCMXCIX

third weird number

the only square pyramidal number that is also a square:

mentioned by Plato as the ideal number of people living in a city, due to its high number of factors

sum of the first 7 factorials: 5913 = 1! + 2! + 3! + … + 6! + 7!

Kaprekar’s constant: take any four-digit number, rearrange its digits to make the largest and smallest possible number, subtract these numbers and repeat. Eventually you will arrive at 6174!

equals

fourth perfect number

has 64 divisors

largest number that cannot be represented as the sum of distinct cubes

largest number that is not the sum of the squares of distinct primes

equals 8 factorial

sum of the factorials of its digits: 40,585 = 4! + 0! + 5! + 8! + 5!

first number, other than 1, that is simultaneously triangular, pentagonal and hexagonal

smallest base 10 cyclic number: multiplied by 2, 3, 4, 5 or 6, it simply rotates is decimal digits

recurring decimal expansion of

the number of spheres touching any other sphere in a 24-dimensional Leech lattice

area of the Pythagorean triangle with sides 693, 1924 and 2045

number of distinct, 5-card poker hands

a coefficient in Archimedes’ cattle problem

number of seconds in a Julian astronomical year (365.25 days)

5th perfect number

the number of distinct magic squares of order 5 (excluding rotations and reflections)

speed of light in vacuum

the largest prime number (in base 10), that you can truncate to produce a sequence of smaller primes: 7, 73, 739, …

the only 10-digit number such that, for every *k* between 1 and 10, its first *k* digits give a number that is a multiple of *k*

6th perfect number

largest perfect power that contains no repeated digits in base ten

7th perfect number

the probability of receiving a complete suit in the game of Bridge

a transcendental number which is an almost integer

8th perfect number, discovered by Euler in 1772

equals

the number of grains of rice required if you place one grain on the first square of a chess board, two on the second, 4 on the third, 8 on the fourth, and so on.

the largest prime number (in base 10), that you can truncate from its beginning to produce a sequence of smaller primes: 7, 37, 137, 9137, …

Belphegor’s Prime

666 with 13 zeroes either side