Mathematically 93

Ninety Three (93)
1. With just a straight cut, a potato can be divided into 93 pieces.

2. It is an odd number with the property that the digit at ten’s place is thrice the digit at one’s place.

3. It is a 32 gonal number.

4. It can be partitioned 47 times with each tern not larger than 2 and 768 times where each term is not larger than 3.

5. It is the first member of the triplet of consecutive semi-primes 93, 94 and 95. A number is called semi primes if it can be expressed as the product of two prime numbers.
93 = 3 x 31 94 = 2 x 47 95 = 5 x 19

6. It is a palindrome number on base 2.
(93)10 = (1011101)2

7. On base 5, it is a repeated digit.
(93)10 = (333)5

8. It can be expressed as the sum of squares of three numbers. Interestingly all the three numbers used are in Arithmetic Progression with common difference 3.
93 = 2^2 + 5^2 + 8^2

9. It is the sum of 6 consecutive numbers.
93 = 13 + 14 + 15 + 16 + 17 + 18

10. It is a Blum integer. A natural number n is a Blum integer if n = p x q is a semi prime and p and q are written in the form of 4x + 3. It is named after computer scientist Manuel Blum.
93 = 3 x 31
where 3 and 31 are prime numbers
31 = 4 x 7 + 3

11. The atomic number of Neptunium is 93.


Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com