Mathematically 97

Ninety Seven (97)

1. It is a 25th prime number and the largest two digit prime number.

2. It is the highest two digit prime number whose cube has no zero.
97^3 = 912673

3. In Georgian calendar there are 97 leap days in every 400 years.

4. It is a 4 dimensional centered cube number.

5. It is a permutable primes. A prime is called permutable if on a given base, the prime always remain a prime despite its digit’s position changed through permutation. It was first studied by H E Richert. 97 and its reverse 79 are primes .The first 10 permutable primes are- 2, 3, 5, 7, 11, 13, 17, 31, 37 and 71.

6. It can be written in the form of – n^4 + (n +1)^4
97 = 2^4 + 3^4

7. The period of reciprocal of 97 = 1/97 is maximum and its length is 96. More interestingly, the first four pairs of its expansion are in Geometric Progression (GP). Alexender Aitken, a professor at Edinburgh University knew it by heart.
1/97 = 0.01 03 09 27 83 50 51 57 52 57 73 19 58 76 28 86 59 79……

8. It is a Proth prime. A Proth prime is written in the form of – k x 2n + 1, where k is an odd positive integer and 2n > k. It is named after the mathematician Francois Proth. The first 10 Proth primes are- 3, 5, 9, 13, 17, 25, 33, 41, 49 and 57.
97 = 3 x 25 + 1

9. The atomic number of Berkelium is 97

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com