5
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits.
Five is the third-smallest prime number, and the second super-prime, since its prime index is prime.[1] Notably, 5 is equal to the sum of the only consecutive primes 2 + 3 and it is the only number that is part of more than one pair of twin primes, (3, 5) and (5, 7),[2][3] also making it the first balanced prime with equal-sized prime gaps above and below it (of 2).[4] 5 is the first safe prime[5] where for a prime is also prime (2), and the first good prime, since it is the first prime number whose square (25) is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes (i.e., 3 × 7 = 21 and 11 × 2 = 22 are less than 25).[6] 11, the fifth prime number, is the next good prime, that also forms the first pair of sexy primes with 5.[7] More significantly, the fifth Heegner number that forms an imaginaryquadratic field with unique factorization is also 11[8] (and the first repunit prime in decimal, a base in-which five is also the first non-trivial 1-automorphic number).[9]
Five is also the second Fermat prime, and the third Mersenne prime exponent, as well as the fourth or fifth Fibonacci number. [14] It is also an Eisenstein prime (like 11) with no imaginary part and real part of the form .[1] It is the first congruent number, as well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple (3, 4, 5).[15] The regular five-sided pentagon is the first regular polygon that does not tile the plane with copies of itself, and it is the largest face that a regular three-dimensional regular Platonic solid can have, as represented in the regular dodecahedron. In general, a conic curve will requires five points in the same way that two points are needed to determine a line.[16]
