60,000 (sixty thousand) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

that comes after 59,999 and before 60,001. It is a round number. It is the value of

\varphi

( 75025).

Selected numbers in the range 60,000–69,999

60,001 to 60,999

* 60,049 =

Leyland number In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, ...

using 3 & 10 (3¹⁰ + 10³) * 60,101 = smallest

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

with period of reciprocal

100 100 or one hundred (Roman numeral: C) is the natural number following 99 and preceding 101. In mathematics 100 is the square of 10 (in scientific notation it is written as 102). The standard SI prefix for a hundred is " hecto-". 100 is the b ...

61,000 to 61,999

* 61,776 = 2⁴ x 3³ x 11 x 13 = 1⁵ + 2⁵ + 3⁵ + 4⁵ + 5⁵ + 6⁵ + 7⁵ + 8⁵. It is an

untouchable number In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back at l ...

, a

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...

, 100-gonal number, and is

polygonal In geometry, a polygon () is a plane (mathematics), plane Shape, figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its ''edge (geometry), edges'' or ''sides''. The p ...

in 6 other ways.

62,000 to 62,999

* 62,208 = 3-

smooth number In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 72 and 15750 = 2 ...

* 62,210 =

Markov number A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are :1 (number), 1, 2 (number), ...

* 62,745 =

Carmichael number In number theory, a Carmichael number is a composite number which in modular arithmetic satisfies the congruence relation: : b^n\equiv b\pmod for all integers . The relation may also be expressed in the form: : b^\equiv 1\pmod for all integers b ...

63,000 to 63,999

* 63,020 =

amicable number In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, ''s''(''a'')=''b'' and ''s''(''b'')=''a'', where ''s''(''n'')=σ('' ...

with 76084 * 63,261 = number of partitions of 43 * 63,360 = inches in a mile * 63,600 = number of free 12-ominoes * 63,750 =

pentagonal pyramidal number A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of s ...

* 63,973 =

64,000 to 64,999

* 64,000 = 40³ * 64,009 = sum of the

cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...

s of the first 22 positive integers * 64,079 =

Lucas number The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence ar ...

* 64,442 = Number of

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

degree intersections on Earth: 360 longitudes * 179 latitudes + 2 poles = 64442. * 64,620 : It is an

, a

, and a number such that pi(64620) = 64620/10.

65,000 to 65,999

* 65,025 = 255², palindromic in base 11 (44944₁₁) * 65,535 = largest value for an unsigned 16-bit integer on a computer. *

65,536 65536 is the natural number following 65535 and preceding 65537. 65536 is a power of two: 2^ (2 to the 16th power). 65536 is the smallest number with exactly 17 divisors (but there are smaller numbers with more than 17 divisors; e.g., 180 ha ...

= 2¹⁶ = 4⁸ = 16⁴ = 256² also 2↑↑4=2↑↑↑3 using

Knuth's up-arrow notation In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperatio ...

, smallest integer with exactly 17 divisors, palindromic in base 15 (14641₁₅), number of directed graphs on 4 labeled nodes *

65,537 65537 is the integer after 65536 and before 65538. In mathematics 65537 is the largest known prime number of the form 2^ +1 (n = 4), and is most likely the last one. Therefore, a regular polygon with 65537 sides is constructible with compass ...

= largest known

Fermat prime In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: 3, 5, ...

* 65,539 = the 6544th prime number, and both 6544 and 65539 have

digital root The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit su ...

of 1; a

regular prime In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli num ...

; a larger member of a

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...

pair; a smaller member of a

cousin prime In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences and in OE ...

pair; a

happy prime In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...

; a weak prime; a middle member of a

prime triplet In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form or . With the exceptions of and , this is the closest possible grouping of ...

, (65537, 65539, 65543); a middle member of a three-term primes in arithmetic progression, (65521, 65539, 65557). * 65,792 =

using 2 & 16 (2¹⁶ + 16²)

66,000 to 66,999

* 66,012 =

tribonacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci seq ...

* 66,049 = 257², palindromic in hexadecimal (10201₁₆) * 66,198 =

Giuga number In number theory, a Giuga number is a composite number n such that for each of its distinct prime factors p_i we have p_i , \left( - 1\right), or equivalently such that for each of its distinct prime factors ''p'i'' we have p_i^2 , (n - p_i). ...

* 66,666 =

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...

67,000 to 67,999

* 67,081 = 259², palindromic in base 6 (1234321₆) * 67,171 = 1⁶ + 2⁶ + 3⁶ + 4⁶ + 5⁶ + 6⁶ * 67,607 = largest of five remaining

Seventeen or Bust PrimeGrid is a volunteer computing project that searches for very large (up to world-record size) prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing (BO ...

numbers in the Sierpiński problem * 67,626 = pentagonal pyramidal number

68,000 to 68,999

* 68,906 = number of prime numbers having six digits. * 68,921 = 41³

69,000 to 69,999

* 69,632 =

using 4 & 8 (4⁸ + 8⁴) * 69,696 =

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

264 __NOTOC__ Year 264 (Roman numerals, CCLXIV) was a leap year starting on Friday of the Julian calendar. At the time, it was known as the Year of the Consulship of Gallienus and Saturninus (or, less frequently, year 1017 ''Ab urbe condita''). The ...

; only known palindromic square that can be expressed as the sum of a pair of

s: 69,696 = 34847 + 34849. * 69,984 = 3-

Primes

There are 878 prime numbers between 60000 and 70000.

References

{{Integers, 10 60000