The Number

Narendra Modi, Prime Minister of India, paid tribute to Srinivasa Ramanujan: “A genius who made a monumental contribution to mathematics, I pay my tributes to the legendary S Ramanujan on his birth anniversary.”

It is Srinivasa Ramanujan’s 127th birth anniversary.

As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for another Mersenne prime 2127 – 1 (2127 – 1), which was discovered by Édouard Lucas in 1876, and held the record for the largest known prime for 75 years – it is still the largest prime ever discovered by hand calculations. Furthermore, 127 is equal to 27 – 1, and because 7 is also a Mersenne prime, this makes 127 a double Mersenne prime.

127 is also a cuban prime of the form p = (x^3 – y^3) / (x – y), x = y + 1. The next prime is 131, with which it comprises a cousin prime. Because the next odd number, 129, is a semiprime, 127 is a Chen prime. 127 is greater than the arithmetic mean of its two neighboring primes, thus it is a strong prime.
127 cannot be written as a sum of a power of 2 and a prime, the next is 149.
127 is a centered hexagonal number.
It is the 7th Motzkin number.
127 is a palindromic prime in nonary and binary.
It is the first nice Friedman number in base 10, since 127 = -1 + 27, as well as binary since 1111111 = (1 + 1)111 – 1 * 1.

Ramanujan would have known THIS NUMBER too.

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