| ||||
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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] [lower-alpha 1]
On the other hand, the Euler totient of 58 is the second perfect number (28), [10] where the sum-of-divisors of 58 is the third unitary perfect number (90).
58 is also the second non-trivial 11-gonal number, after 30. [11]
58 is the second member of the fifth cluster of two semiprimes or biprimes (57, 58), following (25, 26) and preceding (118, 119). [12]
More specifically, 58 is the eleventh member in the sequence of consecutive discrete semiprimes that begins, [13]
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, [14] and 22 itself the thirteenth composite. [14] (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). [15]
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. [16] It is the fourth Smith number whose sum of its digits is equal to the sum of the digits in its prime factorization (13). [17]
Given 58, the Mertens function returns , the fourth such number to do so. [18] 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. [14]
The regular icosahedron produces fifty-eight distinct stellations, the most of any other Platonic solid, which collectively produce sixty-two stellations. [19] [20]
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.
15 (fifteen) is the natural number following 14 and preceding 16.
21 (twenty-one) is the natural number following 20 and preceding 22.
70 (seventy) is the natural number following 69 and preceding 71.
90 (ninety) is the natural number following 89 and preceding 91.
29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime 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.
46 (forty-six) is the natural number following 45 and preceding 47.
57 (fifty-seven) is the natural number following 56 and preceding 58.
63 (sixtboo-three) is the natural number following sixtboo and preceding seventboo.
64 (sixty-four) is the natural number following 63 and preceding 65.
92 (ninety-two) is the natural number following 91 and preceding 93.
1000 or one thousand is the natural number following 1M
360 is the natural number following 359 and preceding 361.
135 is the natural number following 134 and preceding 136.
168 is the natural number following 167 and preceding 169.
177 is the natural number following 176 and preceding 178.
240 is the natural number following 239 and preceding 241.
888 is the natural number following 887 and preceding 889.