View source for 60,000

{{Infobox number
| number = 60000
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'''60,000''' ('''sixty thousand''') is the [[natural number]] that comes after [[50,000#59000 to 59999|59,999]] and before 60,001. It is a round number. It is the value of [[Euler's totient function|<math>\varphi</math>]]([[Fibonacci number|75025]]).<ref>{{Cite OEIS|A065449|2=a(n) = phi(Fibonacci(n))}}</ref>

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

===60,001 to 60,999===
* '''60,049''' = [[Leyland number]]<ref name=A076980>{{cite OEIS|A076980|Leyland numbers}}</ref> using 3 & 10 (3<sup>10</sup> + 10<sup>3</sup>)
* '''60,101''' = smallest [[prime number|prime]] with period of reciprocal [[100 (number)|100]]<ref>{{cite OEIS|A007138|Smallest primitive factor of 10^n - 1. Also smallest prime p such that 1/p has repeating decimal expansion of period n}}</ref>

===61,000 to 61,999===
* '''61,776''' = 2<sup>4</sup> x 3<sup>3</sup> x 11 x 13 = 1<sup>5</sup> + 2<sup>5</sup> + 3<sup>5</sup> + 4<sup>5</sup> + 5<sup>5</sup> + 6<sup>5</sup> + 7<sup>5</sup> + 8<sup>5</sup>.<ref>{{cite OEIS|A000539|Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5}}</ref> It is an [[untouchable number]],<ref name=A005114>{{cite OEIS|A005114|Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function}}</ref> a [[triangular number]],<ref name=A000217>{{cite OEIS|A000217|2=Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n}}</ref> [[hexagonal number]],<ref name=A000384>{{cite OEIS|A000384|2=Hexagonal numbers: a(n) = n*(2*n-1)}}</ref> 100-gonal number,<ref>{{cite OEIS|A261276|2=100-gonal numbers: a(n) = 98*n*(n-1)/2 + n}}</ref> and is [[polygonal number|polygonal]] in 6 other ways.

===62,000 to 62,999===
* '''62,208''' = 3-[[smooth number]]
* '''62,210''' = [[Markov number]]<ref>{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</ref>
* '''62,745''' = [[Carmichael number]]<ref name=":1">{{Cite OEIS|A002997|Carmichael numbers}}</ref>

===63,000 to 63,999===
* '''63,020''' = [[amicable number]] with 76084
* '''63,261''' = number of partitions of 43<ref>{{cite OEIS|A000041|a(n) is the number of partitions of n (the partition numbers)}}</ref>
* '''63,360''' = inches in a mile
* '''63,600''' = number of free 12-ominoes
* '''63,750''' = [[pentagonal pyramidal number]]
* '''63,973''' = [[Carmichael number]]<ref name=":1" />

===64,000 to 64,999===
* '''64,000''' = 40<sup>3</sup>
* '''64,009''' = sum of the [[Cube (algebra)|cube]]s of the first 22 positive integers
* '''[[64,079]]''' = [[Lucas number]]
* '''64,442''' = Number of [[integer]] [[Degree (angle)|degree]] [[Degree Confluence Project|intersections]] on Earth: 360 longitudes * 179 latitudes + 2 poles = 64442.
* '''64,620''' : It is an [[untouchable number]],<ref name=A005114/> a [[triangular number]],<ref name=A000217/> [[hexagonal number]],<ref name=A000384/> and a number such that pi(64620) = 64620/10.<ref>{{cite OEIS|A165689|2=Numbers n such that pi(n) = (1/10)*n}}</ref>

===65,000 to 65,999===
* '''65,025''' = 255<sup>2</sup>, palindromic in base 11 (44944<sub>11</sub>)
* '''[[65,535]]''' = largest value for an unsigned 16-bit [[integer (computer science)|integer on a computer]].
* '''[[65,536]]''' = 2<sup>16</sup> = 4<sup>8</sup> = 16<sup>4</sup> = 256<sup>2</sup> also 2↑↑4=2↑↑↑3 using [[Knuth's up-arrow notation]], smallest integer with exactly 17 divisors, palindromic in base 15 (14641<sub>15</sub>), number of directed graphs on 4 labeled nodes<ref>{{cite OEIS|A002416|2=a(n) = 2^(n^2)}}</ref>
* '''[[65,537]]''' = largest known [[Fermat prime]]
* '''65,539''' = the 6544th prime number, and both 6544 and 65539 have [[digital root]] of 1; a [[regular prime]]; a larger member of a [[twin prime]] pair; a smaller member of a [[cousin prime]] pair; a [[happy prime]]; a [[weak prime]]; a middle member of a [[prime triplet]], (65537,	65539,	65543); a middle member of a three-term primes in arithmetic progression, (65521,	65539,	65557).
* '''65,792''' = [[Leyland number]]<ref name=A076980/> using 2 & 16 (2<sup>16</sup> + 16<sup>2</sup>)

===66,000 to 66,999===
* '''66,012''' = [[tribonacci number]]<ref>{{Cite OEIS|A000073|Tribonacci numbers}}</ref>
* '''66,049''' = 257<sup>2</sup>, palindromic in hexadecimal (10201<sub>16</sub>)
* '''66,198''' = [[Giuga number]]<ref>{{Cite OEIS|A007850|Giuga numbers}}</ref>
* '''66,666''' = [[repdigit]]

===67,000 to 67,999===
* '''67,081''' = 259<sup>2</sup>, palindromic in base 6 (1234321<sub>6</sub>)
* '''67,171''' = 1<sup>6</sup> + 2<sup>6</sup> + 3<sup>6</sup> + 4<sup>6</sup> + 5<sup>6</sup> + 6<sup>6</sup><ref>{{cite OEIS|A031971|2=a(n) = Sum_{k=1..n} k^n}}</ref>
* '''67,607''' = largest of five remaining [[Seventeen or Bust]] numbers in the [[Sierpinski number|Sierpiński problem]]
* '''67,626''' = pentagonal pyramidal number

===68,000 to 68,999===
* '''68,906''' =  number of prime numbers having six digits.<ref>{{Cite OEIS|A006879|Number of primes with n digits.}}</ref>
* '''68,921''' =  41<sup>3</sup>

===69,000 to 69,999===
* '''69,632''' = [[Leyland number]]<ref name=A076980/> using 4 & 8 (4<sup>8</sup> + 8<sup>4</sup>)
* '''69,696''' = [[Square number|square]] of [[264 (number)|264]]; only known [[palindromic number|palindromic square]] that can be expressed as the sum of a pair of [[twin prime]]s: 69,696 = 34847 + 34849.
* '''69,984''' = 3-[[smooth number]]

===Primes===
There are 878 prime numbers between 60000 and 70000.

==References==
{{Reflist}}

{{Integers|10}}

[[Category:Integers|60000]]