Mathematically 73

Seventy Three (73)

1. It is the 21st prime number. It along with the next prime 73 makes a twin prime.

2. It is the smallest number besides 1 which is 1 less than the double of its reverse.
73 = 2 x 37 – 1

3. It is the smallest number with the property that its neighbours can be written as the sum of two squares.
72 = 6^2 + 6^2
73 = 3^2 + 8^2
74 = 5^2 + 8^2

4. It is the smallest prime congruent to 1 modulo 24.
73 ≡ 1 (mod 24)

5. On base 8 it is the only number with repeated unit.
73 = ( 111 ) 8

6. The square root of 73 is 8. 544.. which when summed up gives 21 that is the product of its digit.

(73)^1/2 = 8. 544 and 8 + 5 + 4 + 4 = 7 x 3

7. It is a centered 12 gonal and 24 gonal number.

8. It is the least number of sixth powers needed to represent every possible integer.

9. The atomic number of Tantalum is 73.

10. There is a very interesting puzzle whose final result comes out to be 73.
The steps of the puzzles are--
-a) Take any four digit number
b) Write this number again making a eight digit number
c) Divide this 8 digit number by 137
d) divide the quotient by the 4 digit number taken initially.
The final result will be 73.
Example: - Let the four digit number taken is 1238.
Make this number an eight digit number by writing this number twice, i.e. 12381238.
Divide this big number by 137 and you get the quotient 90374 which when divided by 1238 gives you 73.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com