We all know what a Prime number is, right? But I will still tell you. A prime number is a whole number greater than 1 that can be divided exactly by only two positive whole numbers: 1 and itself.For example 2, 3, 5, 7 and 11 are the first 5 prime numbers.
Two interesting facts about prime numbers. 1 is NOT a prime number because it has only one positive divisor, not two. And 2 is the only even prime number. Every other even number can be divided by 2.
There is no known formula to find a prime number. The most fundamental “formula” is actually a test. For a number n>1, it is prime if it has no divisor among the primes up to square root of n. For example let us take the number 97. The square root of 97 is approximately 9.85. So we just need to test it with numbers 2,3,5 and 7. None divides 97 so it is a prime number.
There is one strange formula for finding primes though. It is n^2 + n + 41. You can substitute n with any number from 1 to 39 and it will always give you a prime number. But the magic ends there. At n = 40, the formula collapses. So there isn’t a simple formula that spits out the next prime on demand.
Now that we have got that out of the way, have you ever wondered which is the largest prime number?
It is called M136279841, and it was discovered by Luke Durant through the Great Internet Mersenne Prime Search (GIMPS) in October 2024. It is the largest known prime number and is equal to 2^(136,279,841) -1.
The fascinating part is that it isn’t just an arbitrary enormous number. It belongs to a special family called Mersenne Primes. And here is the interesting part of Mersenne primes. They have to be numbers of the form 2^P -1 where P is a prime itself. But most prime values of p don’t produce a Mersenne prime. And M136279841 is only the 52nd known Mersenne prime.
Yes if you are interested, you could try finding the 53rd one. 😂
Now you will wonder, why have I taken you down a rabbit hole of prime numbers. Well it started with my hearing Nirvāṇa Ṣaṭkam, also known as Ātma Ṣaṭkam during the morning walk. It is a short and profound hymn traditionally attributed to Ādi Śaṅkarācārya, the great teacher of Advaita Vedānta.
In its six verses, Śaṅkara repeatedly tells us what the Self is not — not the body, senses, mind, intellect, ego, or even our changing emotions and experiences. This is the method of neti, neti—“not this, not this.” In very simple terms, the hymn invites us to ask: If I am not everything that is constantly changing, then who am I?
What is the connection between the largest known Mersenne prime and the Self which Advaita Vedanta talks about?
Even M136279841 can be divided by two positive whole numbers: 1 and itself. With two, distinction appears: one and another, this and that. And once distinction appears, we can begin to explain through comparison, distinctions, relationships and difference.
But think of the number 1.
With 1, there is no further division into smaller whole-number factors. It is the starting point. You cannot explain it by breaking it down into something more fundamental. One is the point at which distinction has not yet arisen. And then I wondered: if Advaita means ‘not two’, is even ‘one’ adequate?
One is still a number, still a concept, still something that can be described.
And in Advaita Vedanta the Self is not even 1. It is अनिर्वचनीयम् — Anirvacanīyam which literally means that which cannot be adequately defined or described.
And that is where I got blown away.
Nirvāṇa Ṣaṭkam, says I am not this, I am not that and now I realised, I am not even 1. In Advaita, non-dual (अद्वैत) does not quite mean “There is one thing.” It actually means “There is no second thing.” That’s a subtle but profound difference.
There is no second reality apart from what you truly are.
And You are That.
तत्त्वमसि — Tat Tvam Asi
Sri, some facts about prime numbers that I didn’t know … thanks for educating!! Once again well researched and beautifully written!! 👌👌
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