5555 - 5

The evolution of 5.

How many 5's are there?

-1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	five
Ordinal	5th (fifth)
Numeral system	quinary
Factorization	prime
Prime	3rd
Divisors	1,5
Greek numeral	Ε´
Roman numeral	V, v
Greek prefix	penta-/pent-
Latin prefix	quinque-/quinqu-/quint-
Binary	1012
Ternary	123
Octal	58
Duodecimal	512
Hexadecimal	516
Greek	ε (or Ε)
Arabic, Kurdish	٥
Persian, Sindhi, Urdu	۵
Ge'ez	፭
Bengali	৫
Kannada	೫
Punjabi	੫
Chinese numeral	五,伍
Korean numerals	다섯,오
Devanāgarī	५
Hebrew	ה
Khmer	៥
Telugu	౫
Malayalam	൫
Tamil	௫
Thai	๕

You took math in high school, right? Read through this and see how many terms are familiar to you.

Five is the third smallest prime number.^[1] Since it can be written as 2² + 1, five is classified as a Fermat prime;^[1] therefore, a regular polygon with 5 sides (a regular pentagon) is constructible with compass and an unmarked straightedge. Five is the third Sophie Germain prime,^[1] the first safe prime, the third Catalan number,^[2] and the third Mersenne prime exponent.^[3] Five is the first Wilson prime and the third factorial prime, also an alternating factorial.^[4] Five is the first good prime.^[5] It is an Eisenstein prime with no imaginary part and real part of the form 3p − 1.^[1] It is also the only number that is part of more than one pair of twin primes. Five is also a super-prime, and a congruent number.^[6]

Five is conjectured to be the only odd untouchable number,^[7] and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

Five is also the only prime that is the sum of two consecutive primes, namely 2 and 3, with these indeed being the only possible set of two consecutive primes.

The number 5 is the fifth Fibonacci number, being 2 plus 3.^[1] It is the only Fibonacci number that is equal to its position. Five is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... (OEIS: A030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.^[8]

5 is the length of the hypotenuse of the smallest integer-sided right triangle.

In bases 10 and 20, 5 is a 1-automorphic number.

Five is the second Sierpinski number of the first kind, and can be written as S2 = (2²) + 1.^[9]

While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group S_n is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K₅, the complete graph with 5 vertices.

There are five known unitary perfect numbers. A sixth unitary number, if discovered, would have at least nine odd prime factors.^[10]

There are five Platonic solids.^[11][1] There are also five regular uniform polyhedron compounds,^[12] five cell-transitive space-filling parallelohedra,^[13] and five abstract polyhedra.^[14]

There are five regular honeycombs in hyperbolic 5-space. ^[15]

A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Five is the only prime number to end in the digit 5 because all other numbers written with a 5 in the ones place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions, unlike expansions with all other prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

There are five exceptional Lie groups.

To see even more about 5...

https://en.wikipedia.org/wiki/5