# What's Special About This Number?

## What's Special About This Number?

Exploring Numbers

http://www2.stetson.edu/~efriedma/numbers.html

primes

graphs

digits

sums of powers

bases

combinatorics

powers/polygonal

Fibonacci

geometry

repdigits

algebra

perfect/amicable

pandigital

matrices

divisors

games/puzzles

0 is the additive identity.

1 is the multiplicative identity.

2 is the only even prime.

3 is the number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar maps.

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass.

8 is the largest cube in the Fibonacci sequence.

9 is the maximum number of cubes that are needed to sum to any positive integer.

10 is the base of our number system.

11 is the largest known multiplicative persistence.

12 is the smallest abundant number.

13 is the number of Archimedian solids.

14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.

15 is the smallest composite number n with the property that there is only one group of order n.

16 is the only number of the form xy = yx with x and y different integers.

17 is the number of wallpaper groups.

18 is the only number (other than 0) that is twice the sum of its digits.

19 is the maximum number of 4th powers needed to sum to any number.

20 is the number of rooted trees with 6 vertices.

21 is the smallest number of distinct squares needed to tile a square.

22 is the number of partitions of 8.

23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

24 is the largest number divisible by all numbers less than its square root.

25 is the smallest square that can be written as a sum of 2 squares.

26 is the only positive number to be directly between a square and a cube.

27 is the largest number that is the sum of the digits of its cube.

28 is the 2nd perfect number.

29 is the 7th Lucas number.

30 is the largest number with the property that all smaller numbers relatively prime to it are prime.

31 is a Mersenne prime.

32 is the smallest non-trivial 5th power.

33 is the largest number that is not a sum of distinct triangular numbers.

34 is the smallest number with the property that it and its neighbors have the same number of divisors.

35 is the number of hexominoes.

36 is the smallest non-trivial number which is both square and triangular.

37 is the maximum number of 5th powers needed to sum to any number.

38 is the last Roman numeral when written lexicographically.

39 is the smallest number which has 3 different partitions into 3 parts with the same product.

40 is the only number whose letters are in alphabetical order.

41 is a value of n so that x2 + x + n takes on prime values for x = 0, 1, 2, ... n-2.

42 is the 5th Catalan number.

43 is the number of sided 7-iamonds.

44 is the number of derangements of 5 items.

45 is a Kaprekar number.

46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.

47 is the largest number of cubes that cannot tile a cube.

48 is the smallest number with 10 divisors.

49 is the smallest number with the property that it and its neighbors are squareful.

50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.

Just a sample - It goes on for awhile

Encyclopedia of Integer Sequences

Notable Properties of Specific Numbers

Number Gossip

Cool Numbers

Properties of the First 5000 Integers

http://www2.stetson.edu/~efriedma/numbers.html

primes

graphs

digits

sums of powers

bases

combinatorics

powers/polygonal

Fibonacci

geometry

repdigits

algebra

perfect/amicable

pandigital

matrices

divisors

games/puzzles

0 is the additive identity.

1 is the multiplicative identity.

2 is the only even prime.

3 is the number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar maps.

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass.

8 is the largest cube in the Fibonacci sequence.

9 is the maximum number of cubes that are needed to sum to any positive integer.

10 is the base of our number system.

11 is the largest known multiplicative persistence.

12 is the smallest abundant number.

13 is the number of Archimedian solids.

14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.

15 is the smallest composite number n with the property that there is only one group of order n.

16 is the only number of the form xy = yx with x and y different integers.

17 is the number of wallpaper groups.

18 is the only number (other than 0) that is twice the sum of its digits.

19 is the maximum number of 4th powers needed to sum to any number.

20 is the number of rooted trees with 6 vertices.

21 is the smallest number of distinct squares needed to tile a square.

22 is the number of partitions of 8.

23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

24 is the largest number divisible by all numbers less than its square root.

25 is the smallest square that can be written as a sum of 2 squares.

26 is the only positive number to be directly between a square and a cube.

27 is the largest number that is the sum of the digits of its cube.

28 is the 2nd perfect number.

29 is the 7th Lucas number.

30 is the largest number with the property that all smaller numbers relatively prime to it are prime.

31 is a Mersenne prime.

32 is the smallest non-trivial 5th power.

33 is the largest number that is not a sum of distinct triangular numbers.

34 is the smallest number with the property that it and its neighbors have the same number of divisors.

35 is the number of hexominoes.

36 is the smallest non-trivial number which is both square and triangular.

37 is the maximum number of 5th powers needed to sum to any number.

38 is the last Roman numeral when written lexicographically.

39 is the smallest number which has 3 different partitions into 3 parts with the same product.

40 is the only number whose letters are in alphabetical order.

41 is a value of n so that x2 + x + n takes on prime values for x = 0, 1, 2, ... n-2.

42 is the 5th Catalan number.

43 is the number of sided 7-iamonds.

44 is the number of derangements of 5 items.

45 is a Kaprekar number.

46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.

47 is the largest number of cubes that cannot tile a cube.

48 is the smallest number with 10 divisors.

49 is the smallest number with the property that it and its neighbors are squareful.

50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.

Just a sample - It goes on for awhile

Encyclopedia of Integer Sequences

Notable Properties of Specific Numbers

Number Gossip

Cool Numbers

Properties of the First 5000 Integers

**Skwirlinator**- Posts : 87

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