 
There are 5 Platonic solids (convex regular polyhedra).
The smallest prime in the first sexy prime pair (5, 11). Note that it is "sexy" since sex is the Latin word for six. [Wilson]
The first prime of the form 6n - 1.
Provably the only prime that is a member of two pairs of twin primes. [Pallo]
55 = 38 + 39 + 40 + ... + 87. [Dutta]
There are no known Wall-Sun-Sun primes greater than 5.
1/2 + 1/3 + 1/5 exceeds 1.
122334 + 5 are prime. [Kulsha]
The smallest balanced prime.
The 5th Mersenne prime is -1 + 23 * 45.
5 is believed to be the only odd untouchable number.
5 starts the smallest set of prime quadruplets, i. e.,
(p, p + 2, p + 6, p + 8) are all prime. [Murthy]
5 = 3! - 2! + 1!
The smallest Wilson prime.
The mineral apatite is 5 on Mohs' hardness scale.
A cryptarithm is a type of mathematical puzzle in which most or all of the digits in a mathematical expression are substituted by letters or other symbols. In the case of XZY + XYZ = YZX, the value of Z must equal 5.
The 5th Fibonacci number.
4p - 3 is prime for p = 2, 3, 5, 7 and 11 (the first 5 consecutive primes).
In 1769 Lambert noted that the number of the digits of the repetend of a repeating decimal, 1/a,
divides a-1 for a = 3 or a prime greater than 5.
The only prime solution to the "triangle = square pyramid " problem, which involves
the equation 3(2y + 1)2 = 8x3 + 12x2 + 4x + 3.
Any Lucas number L5p, for any prime p greater than or equal to 5, has at least two distinct primitive prime factors. [Jarden]
n! never ends in 5 zeros. Note that the first 5 terms in the sequence of numbers of zeros that n! never ends in are all prime. The set includes 5, 11, 17, 23, and 29.
The only prime that is the sum of "Siamese twins," i.e., 2 and 3, which are the only pair of primes that are conjoined (have no composite between them). [Gevisier]
WCYB5 in Bristol, Virginia, has been rated America's number one television station.
Subfactorial 5 is palindromic.
7 * 10n + 1 and 9 * 10n + 7 are prime for n = 1 to 5. [Luhn]
5 requires 5 steps to reach 1 in the 3x + 1 (or Collatz) Problem. Paul Erdős said about the Collatz Conjecture: "Mathematics is not yet ready for such problems."
5 is close to 6(Phi2)/ . [Moody]
A limerick is a light humorous or nonsensical verse of 5 lines that usually has the rhyme scheme aabba. [Luhn]
The fewest number of moves for pawn promotion to occur in chess. [Rachlin]
The smallest odd prime equal to the sum of two squares and
to the arithmetic mean of two squares. [Capelle]
The word PRIME contains 5 letters. [Russell]
5 is the 5th digit in the decimal expansion of = 3.1415.... [Gupta]
Every type of worm has 5 hearts to pump blood through it's long body. [Gilkes]
Many scientists consider information as the 5th dimension. [Luhn]
The number of seconds per hour divided by 5 factorial equals 5 primorial. [Luhn]
Euclid gave 5 postulates of plane geometry. [McCranie]
The American 5-cent piece called a "nickel" weighs 5.000 grams. It used to be made of nickel but is now mostly a copper alloy. [Lee]
5 is unique in that it is the sum of all primes less than 5. [Luhn]
The most cars have room for 5 people. [Luhn]
Some giraffe species have five horns on their heads. [Poo Sung]
Alan Turing's Erdős number. [Croll]
USA, UK, France, China, and Russia are 5 permanent members of the UN Security Council. [Poo Sung]
Mozart mastered his first musical composition before the age of 5. [Tallarico]
The only prime which is the difference of two prime squares. [Gupta]
The smallest safe prime. [Russo]
The smallest good prime. [Russo]
Smallest prime p such that Floor[e^p+1] is prime. [Russo]
There are currently (August 2002) 5 known Mersenne primes with a prime number of digits. [Rupinski]
5 is the smallest first member of a twin primes pair (a, b) such that (a + b) +/- 1 is a second Twin primes pair (c, d). [De Geest]
If you sum squares like 0^2 + 1^2 = 1, 0^2 + 1^2 + 2^2 = 5, 0^2 + 1^2 + 2^2 + 3^2 = 14, etc., it can be proven that the only prime you ever get for a sum is 5. [Burns]
There are 5 vowels in the English language: a, e, i, o and u. [Wagler]
Is "abstemious" the only English word which uses all 5 vowels just once in alphabetical order and contains the same number of consonants? [Bown]
5! + 5 = 53. [Woep]
Each 2^{2^n}-5 with n>3 cannot be the sum of two prime powers. [Zhi-Wei Sun]
The only prime digit in which a perfect square can end. [Gupta]
Several of The Prime Pages have been peer reviewed by the staff at MERLOT (Multimedia Educational Resource for Learning and Online Teaching) and rated 5 out of 5 in all categories.
The smallest prime comparable to all minimal primes in base 2. [Rupinski]
The first 5 open-end aliquot sequences are the so-called "Lehmer five."
5 is unique in that it is the only odd integer that can be expressed as the sum of two consecutive primes. [King]
The sum of all minimal primes in base 2 is prime. [Rupinski]
The largest minimal prime in base 4. [Rupinski]
Fn = 2^(2^n) + 1 are semiprimes for n = 5, 6, 7, and 8. [De Geest and
Honaker]
5 is unique in that it is the first and only prime with 5 as the last digit. [Gust]
Ackerman's function A(m,n) is never prime for any m > 5. [Hartley]
The 5 Olympic rings overlap to create 3^2 separate areas. Note the first three primes in reverse order. [Miglinci]
5 stays in the middle of every magic square of order 3. Note that the magical sum for such a square is 5*3. [Laurv]
There are 5 books in the Bible with exactly 5 chapters. [Hartley]
5 is the only prime number surrounded by four prime factors (2*2, 5, 2*3). [Wagler]
5 is the smallest pentagonal prime. [Capelle]
The smallest number of queens needed to attack every square on a standard chess board. [Patterson]
Phi can be expressed as (5^.5*.5+.5). Perhaps 5 should be spelled phive. [Patterson]
!5 - 1 is prime. Note that !5 represents subfactorial 5. [Gupta]
5 = 12 in base 3. There is no other prime p that can be expressed as p = 12...n in base n+1, because p has n as a factor if n is odd, or n/2, if n is even. [Necula]
The smallest odd prime Thabit number. Arab mathematician Thabit ibn Qurra discovered a rule for finding amicable pairs based on these numbers (of the form 3 * 2n - 1) before his death in Baghdad in 901.
An ace is a military aircraft pilot who has destroyed 5 or more enemy aircraft. [Richthofen]
5 is the answer to the question asked at the very end of the mathematics quiz show in the movie Little Man Tate.
The only sexy prime quintuplet starts at 5. I.e, 5+6, 5+6+6, 5+6+6+6 and 5+6+6+6+6 are also prime. [Opao]
The only single-digit prime with a prime ASCII code: 35 (in base 16) = 53. [Necula]
One of the best-known perfumes, Chanel N°5, was introduced by Gabrielle "Coco" Chanel on May 5, 1921.
"e" is the fifth letter of the English alphabet. [Dunham]
5 is the smallest number that appear in two twin Pythagorean triplets: (3, 4, 5) and (5, 12, 13). [Laurv]
5 is the smallest hypotenuse of a Pythagorean triangle (3^2 + 4^2 = 5^2). [Laurv]
The Virginia Tech Supercomputer (unofficially nicknamed Big Mac) is a computer cluster composed of Apple G5 machines. Note that it cost only 5 million dollars to build.
In esoteric writings, 5 is the number of magic that travels through cycles of four (e.g., seasons). [Woep]
The length of the side of a basic pantactic square (see Brian Astle, "Pantactic Squares" Math Gazette 1965, pp.144-52). [Astle]
Henry Ford is said to have paid his assembly-line workers an unheard of $5.00 a day, in 1914. [McAlee]
A Star Fish has 5 pointy legs. [McAlee]
All the solutions of n = (2n) are nonnegative integers less than 5. [Firoozbakht]
5 is the first Centered Square Prime Number. [Post]
The first prime Apéry number. [Post]
5 is the smallest prime numerator of a Bernoulli number. [Post]
The only prime that is sandwiched between two semiprimes. [Gupta]
5 is the smallest nontrivial Euler number. [Terr]
"All number of the form n^4+4 , except 5, is the product of
two integers." [Germain]
Evariste Galois was the first to show that equations of
degree 5 cannot be solved by radicals. [Beedassy]
Divisibility test for 5: A number is divisible by 5 if it
ends in 0 or 5.
A mathematical analysis says that our universe may well be a 5D black hole (General Relativity and Gravitation, Volume 37, p.1339).
The masculine marriage number to the Pythagoreans, uniting the first female number and the first male number by addition.
There are 5 families of butterflies. [Capelle]
5 is written with 5 lines on a calculator.
5 is the only prime written with an equal (prime) number of
distinct vowels and consonants. [Beedassy]
5 equals the cube root of (5! + 5). [Silva]
Eugen J. Ionascu and collaborators were the first to establish that there can be no more than 5 Heron triangles (i.e., integer-sided triangles with integral areas) with two fixed prime sides. [Beedassy]
The only temperatures that are prime integers in both Celsius and Fahrenheit are +/- 5 °C (41 °F and 23 °F).
The only prime member of a Ruth-Aaron pair. [Caldwell]
The sum of the reciprocals of the primes is infinite, but
the sum of the reciprocals of the known primes is less than
5 and will always be so! [Caldwell]
Every positive integer can be written as
x2+2y2+7z2+11w2, except for 5. [Halmos1938] [Caldwell]
No perfect Golomb ruler exists for 5 or more ticks.
The difference between the number of primes less than ten thousand (1229) and the number of twin prime pairs less than one hundred thousand (1224).
Most humans have 5 fingers in the hands and feet. [Alvino]
The only prime p such that p divides the p^th Fibonacci
number. All other primes divide either the (p-1)^st
Fibonacci number if p = 1,4 mod 5 or (p+1)^st Fibonacci
number if p = 2,3 mod 5. [Rupinski]
"Facetious" contains all 5 vowels of the English language
in alphabetical order. [Giberson]
Adams was the first with a prime number of letters in his
last name, among the Presidents of the United States of
America. Obama is the most recent. [Post]
There is one chance in 5 for a random number on the number
line to be an
evil number. [Beedassy]
The only prime number of terms for which the series of
squares equals a triangular number : 12 +
22 + 32 + 42 +
52 = 1 + 2 + 3 + ... + 8 + 9 + 10. [Beedassy]
Boron has 5 letters and 5 protons in its atomic nucleus.
5 is the only prime in the middle of a pair of cousin primes. [Silva]
For the first five primes we have prime(2)*prime(4) - prime(1)*prime(3) = prime(5). It's interesting that we also have 2*4 - 1*3 = 5. [Firoozbakht]
The only prime that is equidistant from a pair of primes by
a prime (2) and also from a pair of nonprimes by a nonprime
(4). [Beedassy]
n=5 is the first prime for which an n-by-n chessboard knight's tour graph is traceable, i.e., a knight's path exists. Note that 2^3 paths on the 5-by-5 chessboard are symmetric and 3^3*4^3 total paths that exist (Kraitchik, 1942). [Krug]
The arithmetic average of the first sixteen digits of the
decimal expansion of . [Silva]
5 7 11
11 13 17
17 19 23
The smallest prime (the only prime which ends with 5) in a special 3-by-3 prime square.
column 1: lesser primes of the form 3!*k-1 of 3 consecutive
twin prime couples, also smallest prime of 3 prime triples
in 1st arithmetic sequence (AS) with d=1*2*3=6.
column 2: bigger primes of form 3!*k+1 of 3 consecutive
twin prime couples in AS with d=3! (faculty).
column 3: larger member
p of three consecutive cousin primes (p-4,p) all of form
3n-1 and consecutive numbers n where (n!+3)/3 is prime.
line 1: 1st prime triple sums to prime 23=5+7+11, also
consecutive numbers n of partitions of n.
line 2: 3rd triple primes sum to prime 41=11+13+17,
smaller primes p of 3 consecutive twin prime pairs, 3
consecutive indices of prime Fibonacci numbers and p+3!
prime too.
line 3: 5th triple 17+19+23=7^2, a square and Chen primes p
(i.e. p+2 is prime or a biprime), 3 consecutive primes of
sexy prime pairs.
diagonal 1: 5+13+23 sum to prime 41, first 3 primes with
property (3*n)th prime: 5=p(3), 13=p(2*3), 23=p(3*3).
diagonal 2: is line 2 ... you are invited to find more! [K. Krug]
sigma(5!) = 2#*3#*5#. [Wesolowski]
5 = 012 + 021 +
102 + 120 +
201 + 210 [Poo Sung]
The first number to appear between composites. [Silva]
The smallest number n such that neither n!+1 nor n!-1 is
prime. [Silva]
The number of known strobogrammatic squares. The number of
distinct digits to write them. [Capelle]
The largest Pell number (coincidentally prime) of the
form x2 + 1. Note that 5 =
22 + 1, where 1 and 2 are the
two other Pell numbers of this form. [Capelle]
The only prime of the form 4n + n4, where n is a positive
integer. [Capelle]
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