Thursday, August 7, 2014

4500

4500 = 2 x 2 x 3 x 3 x 5 x 5 x 5. It has exactly three distinct prime factors, none of which is greater than 5 (A143207).

4500 is the smallest base in which KJIHGFEDCBA987654321 is a prime. All shorter such strings achieve prime status in mch smaller bases (192 is the maximum required). Not until the string (110)(109)(108) . . . 321 is a higher base required.

4500 is the number of regions formed when all diagonals are drawn in a regular 20-gon (A007678).

4500 is a concentric icosagonal number (A195148).

4500 can be represented in bases 2, 3, 4, and 5 using only the digits 0, 1, and 2. It is 3421 in base 11.

4500 has two representations as a sum of two squares: 4500 = 122 + 662 = 302 + 602.


Source: Prime Curios!

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