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
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
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
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