Primes

We all know about prime numbers. I was just thinking about them, and one question came up.

What about primes that occur at prime(th) location in the list of prime numbers? And, how about that location also occurring at prime(th) location and so on..

For example, 7 is a prime number; it is 4th prime number after 2, 3 and 5. But 4 is not a prime so, 7 would not figure in that list. But 5 will work, because 5 is 3rd prime.

i.e., find all prime numbers that are 'positionally recursive primes'. Let p be a prime and pos(p) denote the position of p in the list of primes.

Then, we want all p such that
pos(p), pos(pos(p)),...
and so on.. are all primes.

It seems that this list can be generated. The smallest prime is 2 but it is 1st prime. So, 2 is not the candidate. 3 is 2nd prime and 2 itself is prime. Next number in the sequence would be 5 (3rd prime). Next will be 11 (5th prime) and so on...

Here are few initial numbers in the list:
3
5
11
31
127
709
5381
52711
648391
9737333
174440041
3657500101
88362852307
2428095424619
...


Now, an amazing co-incidence is that 5381 is my extension number.

Numbers

Some thoughts about numbers:

It is amazing that numbers arise in our minds and hence the mathematics and hence logic, rationality, science and so on...

Have you ever wondered what is 1, what is 2 and so on...? Even more baffling is what is 0?

No matter how we rename them, 1 is 1 and 2 is 2 and they are different and everybody EXACTLY knows this. Isn't that beautiful?

In this fuzzy world, numbers are the only truth, uncompromising, pristine, pure and precise. Numbers are the only solace. Numbers are divine.

O Manikarnika Ghat

O Manikarnika Ghat,
Grasp me in your fire..save me from life's ire..
with the Ganga washing my feet, the end looks neat,
Shiva whispering in my ear, liberation seems so near..

With the evening sun in my eye, earth in my hand, water in my mouth,
with sky overlooking my cremation, I call you Agni and Vayu my friends,
come soon, let's meet for one final time, sit together and rhyme with
the Veda hymn,
It is a beautiful evening today in Kashi.