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60,000

FieldValue
number60000

60,000 (sixty thousand) is the natural number that follows 59,999 and precedes 60,001. 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 using 3 & 10 (310 + 103)
  • 60,101 = smallest prime with period of reciprocal 100

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, a triangular number, hexagonal number, 100-gonal number, and is polygonal in 6 other ways.

62,000 to 62,999

  • 62,208 = 3-smooth number
  • 62,210 = Markov number
  • 62,745 = Carmichael number

63,000 to 63,999

  • 63,020 = amicable number 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
  • 63,973 = Carmichael number

64,000 to 64,999

  • 64,000 = 403
  • 64,009 = sum of the cubes of the first 22 positive integers
  • 64,079 = Lucas number
  • 64,442 = Number of integer degree intersections on Earth: 360 longitudes * 179 latitudes + 2 poles = 64442.
  • 64,620 : It is an untouchable number,

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 = 216 = 48 = 164 = 2562 also 2↑↑4=2↑↑↑3 using Knuth's up-arrow notation, smallest integer with exactly 17 divisors, palindromic in base 15 (1464115), number of directed graphs on 4 labeled nodes
  • 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 using 2 & 16 (216 + 162)

66,000 to 66,999

  • 66,012 = tribonacci number
  • 66,049 = 2572, palindromic in hexadecimal (1020116)
  • 66,198 = Giuga number
  • 66,666 = repdigit

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 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 = Leyland number using 4 & 8 (48 + 84)
  • 69,696 = square of 264; only known palindromic square that can be expressed as the sum of a pair of twin primes: 69,696 = 34847 + 34849.
  • 69,984 = 3-smooth number

Primes

There are 878 prime numbers between 60000 and 70000.

References

References

  1. {{Cite OEIS. A065449
  2. {{cite OEIS. A076980. Leyland numbers
  3. {{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
  4. {{cite OEIS. A000539. Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5
  5. {{cite OEIS. A005114. Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function
  6. {{cite OEIS. A000217
  7. {{cite OEIS. A000384
  8. {{cite OEIS. A261276
  9. {{Cite OEIS. A002559. Markoff (or Markov) numbers
  10. {{Cite OEIS. A002997. Carmichael numbers
  11. {{cite OEIS. A000041. a(n) is the number of partitions of n (the partition numbers)
  12. A165689
  13. {{cite OEIS. A002416
  14. {{Cite OEIS. A000073. Tribonacci numbers
  15. {{Cite OEIS. A007850. Giuga numbers
  16. {{cite OEIS. A031971
  17. {{Cite OEIS. A006879. Number of primes with n digits.
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