Closing in on 10 000

As we close in on 10 000 hits on this blog...

I thought it might be good to steal some ideas from a web page "What's Special About this Number?"

http://www2.stetson.edu/~efriedma/numbers.html

Yes - I e-mailed the author of the site and got permission to do this. Thanks Erich!

And I edited the list a bit to pick out the numbers that I understood...

So here's some interesting numbers between 9500 and 9999

9500 is a hexagonal pyramidal number.
9513 is the smallest number without increasing digits that is divisible by the number formed by writing its digits in increasing order.
9519 has a 4^th power that is the sum of four 4^th powers.
9538 is a value of n for which 4n and 5n together use each digit exactly once.
9541 is a value of n for which n and 8n together use each digit 1-9 exactly once.
9542 is the number of ways to place a non-attacking white and black pawn on a 11×11 chessboard.
9551 has the same digits as the 9551^st prime.
9552 and the following 34 numbers are composite.
9563 = 9 + 5555 + 666 + 3333.
9568 = 9 + 5 + 666 + 8888.
9576 = 19!!!!! 
9592 is the number of primes with 5 or fewer digits.
9602 has the property that if each digit is replaced by its square, the resulting number is a square.
9615 is the smallest number whose cube starts with 5 identical digits.
9627 is a value of n for which n and 5n together use each digit 1-9 exactly once.
9629 is a value of n for which 2n and 7n together use each digit exactly once.
9632 is the number of different arrangements of 4 non-attacking queens on a 4×14 chessboard.
9639 has a 4^th power that is the sum of four 4^th powers.
9643 is the smallest number that can not be formed using the numbers 2⁰, 2¹, ... , 2⁷, together with the symbols +, –, × and ÷.
9648 is a factor of the sum of the digits of 9648⁹⁶⁴⁸.
9653 = 99 + 666 + 5555 + 3333.
9658 = 99 + 666 + 5 + 8888.
9677 is a prime that remains prime if any digit is deleted.
9701 has a square whose digits each occur twice.
9721 is the largest prime factor of 1234567.
9723 is a value of n for which n and 5n together use each digit 1-9 exactly once.
9724 = 1111 in base 21.
9728 can be written as the sum of 2, 3, 4, or 5 positive cubes.
9753 is a value of n for which 4n and 5n together use each digit exactly once.
9767 is the largest 4 digit prime composed of concatenating two 2 digit primes.
9768 = 2 × 22 × 222.
9779 has a square root that has four 8's immediately after the decimal point.
9786 has a square whose digits each occur twice.
9790 is the number of ways to place 2 non-attacking kings on a 12×12 chessboard.
9793 is the smallest number that can be written as the sum of 4 distinct positive cubes in 5 ways.
9796 has the property that dropping its first and last digits gives its largest prime factor.
9797 is the product of two consecutive primes.
9801 is 9 times its reverse.
9841 = 111111111 in base 3.
9856 is the number of ways to place 2 non-attacking knights on a 12×12 chessboard.
9862 is the number of knight's tours on a 6×6 chessboard.
9872 = 8 + 88 + 888 + 8888.
9876 is the largest 4-digit number with different digits.
9878 has a 10^th power whose first few digits are 88448448....
9900 = 10011010101100₂ = 9900₁₀ = 1881₁₉ = 1199₂₁, each using two digits the same number of times.
9920 is the maximum number of regions a cube can be cut into with 39 cuts.
9933 = 441 + 442 + . . . + 462 = 463 + 464 + . . . + 483.
9945 = 17!!!!.
9973 is the largest 4-digit prime.
9999 is a Kaprekar number.