| ||||
---|---|---|---|---|
Cardinal | sixty-one | |||
Ordinal | 61st (sixty-first) | |||
Factorization | prime | |||
Prime | 18th | |||
Divisors | 1, 61 | |||
Greek numeral | ΞΑ´ | |||
Roman numeral | LXI | |||
Binary | 1111012 | |||
Ternary | 20213 | |||
Senary | 1416 | |||
Octal | 758 | |||
Duodecimal | 5112 | |||
Hexadecimal | 3D16 |
61 (sixty-one) is the natural number following 60 and preceding 62.
61 is the 18th prime number, and a twin prime with 59. As a centered square number, it is the sum of two consecutive squares, . [1] It is also a centered decagonal number, [2] and a centered hexagonal number. [3]
61 is the fourth cuban prime of the form where , [4] and the forth Pillai prime since is divisible by 61, but 61 is not one more than a multiple of 8. [5] It is also a Keith number, as it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61, ... [6]
61 is a unique prime in base 14, since no other prime has a 6-digit period in base 14, and palindromic in bases 6 (1416) and 60 (1160). It is the sixth up/down or Euler zigzag number.
61 is the smallest proper prime, a prime which ends in the digit 1 in decimal and whose reciprocal in base-10 has a repeating sequence of length where each digit (0, 1, ..., 9) appears in the repeating sequence the same number of times as does each other digit (namely, times). [7] : 166
In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number [8] (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).
There are sixty-one 3-uniform tilings, where on the other hand, there are one hundred and fifty-one 4-uniform tilings [9] (with 61 the eighteenth prime number, and 151 the thirty-sixth, twice the index value). [10] [lower-alpha 1]
Sixty-one is the exponent of the ninth Mersenne prime, [15] and the next candidate exponent for a potential fifth double Mersenne prime: [16]
61 is also the largest prime factor in Descartes number, [17]
This number would be the only known odd perfect number if one of its composite factors (22021 = 192 × 61) were prime. [18]
61 is the largest prime number (less than the largest supersingualar prime, 71) that does not divide the order of any sporadic group (including any of the pariahs).
The exotic sphere is the last odd-dimensional sphere to contain a unique smooth structure; , and are the only other such spheres. [19] [20]
Sixty-one is:
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.
11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
23 (twenty-three) is the natural number following 22 and preceding 24.
32 (thirty-two) is the natural number following 31 and preceding 33.
31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.
37 (thirty-seven) is the natural number following 36 and preceding 38.
58 (fifty-eight) is the natural number following 57 and preceding 59.
63 (sixty-three) is the natural number following 62 and preceding 64.
64 (sixty-four) is the natural number following 63 and preceding 65.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
127 is the natural number following 126 and preceding 128. It is also a prime number.
500 is the natural number following 499 and preceding 501.
2000 is a natural number following 1999 and preceding 2001.
135 is the natural number following 134 and preceding 136.
1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001. With a number, "billion" can be abbreviated as b, bil or bn.
In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 is a pandigital number in base 10. The first few pandigital base 10 numbers are given by :
168 is the natural number following 167 and preceding 169.
271 is the natural number after 270 and before 272.
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.