90,000 Explained

Number:

90000

90,000 (ninety thousand) is the natural number following 89,999 and preceding 90,001. It is the sum of the cubes of the first 24 positive integers, and is the square of 300.

Selected numbers in the range 90,000–99,999

90,625 = the only five-digit automorphic number: 90625² = 8212890625^[1]
91,125 = 45³
91,144 = Fine number^[2]
92,205 = number of 23-bead necklaces (turning over is allowed) where complements are equivalent
92,706 = There is a math puzzle called KAYAK + KAYAK + KAYAK + KAYAK + KAYAK + KAYAK = SPORT, where each letter represents a digit. When one solves the puzzle, KAYAK = 15451, and when one added this up, SPORT = 92,706. ^[3]
93,312 = Leyland number: 6⁶ + 6⁶.^[4] Also a 3-smooth number.
94,249 = palindromic square: 307²
94,932 = Leyland number: 7⁵ + 5⁷
95,121 = Kaprekar number: 95121² = 9048004641; 90480 + 04641 = 95121^[5]
95,420 = number of 22-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
96,557 = Markov number: 5² + 6466² + 96557² = 3 × 5 × 6466 × 96557^[6]
97,336 = 46³, the largest 5-digit cube
98,304 = 3-smooth number
99,066 = largest number whose square uses all of the decimal digits once: 99066² = 9814072356. It is also strobogrammatic in decimal.
99,856 = 316², the largest 5-digit square
99,991 = largest five-digit prime number
99,999 = repdigit, Kaprekar number: 99999² = 9999800001; 99998 + 00001 = 99999

Primes

There are 879 prime numbers between 90000 and 100000.

Notes and References

Web site: Sloane's A003226 : Automorphic numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-16.
1 on an n-set; also number of ordered rooted trees with n edges having root of even degree. 2022-06-01.
Web site: KAYAK Puzzle - Solution .
Web site: Sloane's A076980 : Leyland numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-16.
Web site: Sloane's A006886 : Kaprekar numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-16.
Web site: Sloane's A002559 : Markoff (or Markov) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-16.