Once a boy wanted to steal lemons from a lady’s garden when she was away on a holiday. The garden was being guarded by two guards that posed a difficult situation for the boy. The boy went to the first guard, and offered a share of what he would steal. Interestingly, the first guard agreed; but in return, demanded for one half of the total number of lemons that the boy would steal. In an effort of negotiation, the boy asked for taking one from the lemons that would go to guard’s share. Considering it a small number, in fact, the smallest natural number, guard readily agreed.

Encouraged by his success of convincing the first guard, the boy met the second and offered the same deal; and the guard agreed too.

The deal was made, and the boy moved into the garden and plucked the lemons. On the way, he shared fifty per cent of the lemons; and took back one each from the guards.

While the boy moved out of the premises, he was very happy as he did not give any lemon effectively to any of these guards. Because, he had plucked only two lemons. In fact, he was elated of his intellect of fooling guards irrespective of the number of guards who might have been present in the premises in a possibly more difficult situation.

The story is not new, nor did it occur to me naturally. It was reminded (narrated) to me a couple of days ago by my nine years-old son who was demonstrating the power of the smallest prime number while we were engaged in a discussion about interesting behaviours of this set of natural numbers.

But the series of events in the story involved several serious considerations. The number involved in the transaction is very small. Moreover, none of the guard could appropriate any lemon or bribe. Does it mean that the guards were not corrupt? Can a small transaction not show the actual character of the person responsible for the transaction? Or, will the facilitator for a corrupt activity not be accounted if he does not get any return from the transaction? Or, shall we respect the integrity of the guards who stuck to their commitment of the deal that they had agreed before?

If we account for individual state of number of lemons at a given time, we have a step-function; and for numbers at the end of each transaction, a constant function. If we extend the event to a large series of events involving the process of sharing two lemons and return one back, one event at a time, we may end of in declaring the compliance to natural empathy for conservation of quantity, foolishness of intellect, disrespect to individual identity, and above all, corruption for the boy or integrity for the deal. The process has all the ingredients of collective behaviour, or regressively speaking, crowd-behaviour.

It is always very amazing to see the power of the smallest prime number who only see the Identity (1) except the self, as normal for any prime number, to divide itself, can demonstrate a multitude of intricate aspects of human characters and functional patterns in society that can be extended peacefully, even for a large number of people. In fact, the number can affect more than two people at least, and can be extended to any number ideally, while dealing with its division. Perhaps that is why the prime numbers are beautiful how small they are.


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