GOTW- Counting - Page 7

56 🤢

Lik stole my number 😡

Fifty-seven is the sixteenth discrete semiprime and the sixth in the (3.q) family. With 58 it forms the fourth discrete bi-prime pair. 57 has an aliquot sum of 23 and is the first composite member of the 23-aliquot tree. Although 57 is not prime, it is jokingly known as the "Grothendieck prime" after a story in which Grothendieck supposedly gave it as an example of a particular prime number.^[1]

As a semiprime, 57 is a Blum integer since its two prime factors are both Gaussian primes.

57 is a 20-gonal number. It is a Leyland number since 2⁵ + 5² = 57.

57 is a repdigit in base 7 (111).

See also 57-cell.

Sheils You don't know to count what a pity 😆

Fifty-eight has an aliquot sum of 32 and is the second composite member of the 83-aliquot tree.

Fifty-eight is the sum of the first seven prime numbers, an 11-gonal number, and a Smith number. Given 58, the Mertens function returns 0.

There is no solution to the equation x - f(x) = 58, making 58 a noncototient. However, the sum of the totient function for the first thirteen integers is 58.

Fifty-nine is the 17th smallest prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form . Since 15! + 1 is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime.

It is also a highly cototient number.

There are 59 stellations of the icosahedron.^[1]

59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13# + 1 = 2 * 3 * 5 * 7 * 11 * 13 + 1 = 59 * 509.

Originally posted by: -Nakshatra-

Fifty-seven is the sixteenth discrete semiprime and the sixth in the (3.q) family. With 58 it forms the fourth discrete bi-prime pair. 57 has an aliquot sum of 23 and is the first composite member of the 23-aliquot tree. Although 57 is not prime, it is jokingly known as the "Grothendieck prime" after a story in which Grothendieck supposedly gave it as an example of a particular prime number.^[1]

As a semiprime, 57 is a Blum integer since its two prime factors are both Gaussian primes.

57 is a 20-gonal number. It is a Leyland number since 2⁵ + 5² = 57.

57 is a repdigit in base 7 (111).

See also 57-cell.

Sheils You don't know to count what a pity 😆

Why did u post 57 again u dumb girl

Sixty is a composite number with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, making it also a highly composite number. Because 60 is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is also an excessive number with an abundance of 48. Being ten times a perfect number, 60 is a semiperfect number.

Sixty is the smallest number divisible by the numbers 1 to 6. (There is no smaller number divisible by the numbers 1 to 5). 60 is the smallest number with exactly 12 divisors. It is one of only 7 integers that have more divisors then any number twice itself (sequence A072938 in OEIS), and is one of only 6 that are also lowest common multiple of a consecutive set of integers from 1, and one of the 6 that are divisors of every highly composite number higher than itself.(sequence A106037 in OEIS)

Sixty is the sum of a pair of twin primes (29 + 31), as well as the sum of four consecutive primes (11 + 13 + 17 + 19). It is adjacent to two prime numbers (59,61). It is also the smallest number which is the sum of two odd primes in 6 ways.^[1]

The smallest non-solvable group (A₅) has order 60.

There are four Archimedean solids with 60 vertices: the truncated icosahedron, the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron. The skeletons of these polyhedra form 60-node vertex-transitive graphs. There are also two Archimedean solids with 60 edges: the snub cube and the icosidodecahedron. The skeleton of the icosidodecahedron forms a 60-edge symmetric graph.

There are 60 one-sided hexominoes, the polyominoes made from 6 squares.

In geometry, 60 is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the 3 interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees.

Because 60 is divisible by the sum of its digits in base 10, it is a Harshad number.

Originally posted by: sheila1990

Why did u post 57 again u dumb girl

You did a mistake and call me dumb ha ha ha ha what a joke 😆 😆

It is the 18th prime number. The previous is 59, with which it comprises a twin prime. Sixty-one is a cuban prime of the form .

Sixty-one might be the largest prime that divides the product of the next two primes plus 1. If there is a larger such prime, it would have to be greater than 179424673.

61 is 9th Mersenne Prime Exponent. (2⁶¹ - 1 = 2305843009213693951)

Sixty-one is the sum of two squares, 5² + 6², and it is also a centered square number, a centered hexagonal number and a centered decagonal number.

Since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8, 61 is a Pillai prime. In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number (namely 6469693291, 7420738134871 and 1922760350154212639131).

It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61...