| ||||
---|---|---|---|---|
Cardinal | fifty-eight | |||
Ordinal | 58th (fifty-eighth) | |||
Factorization | 2 × 29 | |||
Divisors | 1, 2, 29, 58 | |||
Greek numeral | ΝΗ´ | |||
Roman numeral | LVIII | |||
Binary | 1110102 | |||
Ternary | 20113 | |||
Senary | 1346 | |||
Octal | 728 | |||
Duodecimal | 4A12 | |||
Hexadecimal | 3A16 |
58 (fifty-eight) is the natural number following 57 and preceding 59.
Fifty-eight is the seventeenth semiprime [1] and the ninth with 2 as the lowest non-unitary divisor; thus of the form , where is a higher prime (29).
58 is equal to the sum of the first seven consecutive prime numbers: [2]
This is a difference of 1 from the seventeenth prime number and seventh super-prime, 59. [3] [4] 58 has an aliquot sum of 32 [5] within an aliquot sequence of two composite numbers (58, 32, 13, 1, 0) in the 13-aliquot tree. [6] There is no solution to the equation , making fifty-eight the sixth noncototient; [7] however, the totient summatory function over the first thirteen integers is 58. [8]
58 is also the second non-trivial 11-gonal number, after 30. [9]
58 is the second member of the fifth cluster of two semiprimes or biprimes (57, 58), following (25, 26) and preceding (118, 119). [10]
More specifically, 58 is the eleventh member in the sequence of consecutive discrete semiprimes that begins, [11]
58 represents twice the sum between the first two discrete biprimes 14 + 15 = 29, with the first two members of the first such triplet 33 and 34 (or twice 17, the fourth super-prime) respectively the twenty-first and twenty-second composite numbers, [12] and 22 itself the thirteenth composite. [12] (Where also, 58 is the sum of all primes between 2 and 17.) The first triplet is the only triplet in the sequence of consecutive discrete biprimes whose members collectively have prime factorizations that nearly span a set of consecutive prime numbers.
is also semiprime (the second such number for after 2). [13]
The fifth repdigit is the product between the thirteenth and fifty-eighth primes,
58 is also the smallest integer in decimal whose square root has a continued fraction with period 7. [14] It is the fourth Smith number whose sum of its digits is equal to the sum of the digits in its prime factorization (13). [15]
Given 58, the Mertens function returns , the fourth such number to do so. [16] The sum of the first three numbers to return zero (2, 39, 40) sum to 81 = 9 2, which is the fifty-eighth composite number. [12]
The regular icosahedron produces fifty-eight distinct stellations, the most of any other Platonic solid, which collectively produce sixty-two stellations. [17] [18]
With regard to Coxeter groups and uniform polytopes in higher dimensional spaces, there are:
There exist 58 total paracompact Coxeter groups of ranks four through ten, with realizations in dimensions three through nine. These solutions all contain infinite facets and vertex figures, in contrast from compact hyperbolic groups that contain finite elements; there are no other such groups with higher or lower ranks.
58 is the number of usable cells on a Hexxagon game board.
10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.
21 (twenty-one) is the natural number following 20 and preceding 22.
90 (ninety) is the natural number following 89 and preceding 91.
22 (twenty-two) is the natural number following 21 and preceding 23.
27 is the natural number following 26 and preceding 28.
69 is the natural number following 68 and preceding 70. An odd number and a composite number, 69 is divisible by 1, 3, 23 and 69. 69 is a semiprime because it is a natural number that is the product of exactly two prime numbers, and an interprime between the numbers of 67 and 71. Because 69 is not divisible by any square number other than 1, it is categorised as a square-free integer. 69 is also a Blum integer since the two factors of 69 are both Gaussian primes. In number theory, 69 is a deficient number, arithmetic number and a congruent number.
35 (thirty-five) is the natural number following 34 and preceding 36.
34 (thirty-four) is the natural number following 33 and preceding 35.
55 (fifty-five) is the natural number following 54 and preceding 56.
57 (fifty-seven) is the natural number following 56 and preceding 58.
63 (sixty-three) is the natural number following 62 and preceding 64.
92 (ninety-two) is the natural number following 91 and preceding 93.
216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.
177 is the natural number following 176 and preceding 178.
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.
744 is the natural number following 743 and preceding 745.
888 is the natural number following 887 and preceding 889.
14 (fourteen) is a natural number following 13 and preceding 15.
2016 is the natural number following 2015 and preceding 2017.