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**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...*

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**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 2

^{0}, 2

^{1}, ... , 2

^{7}, together with the symbols +, –, × and ÷.

9648 is a factor of the sum of the digits of 9648

^{9648}.

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 = 10011010101100

_{2}= 9900

_{10}= 1881

_{19}= 1199

_{21}, 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.

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