Bapy Biswas wrote:nafistiham wrote:How are you sure that $P_3$ and $P_4$ are prime.It is true that all the primes till $P_2$ do not divide them.But, that does not mean they are primes.A larger prime may divide them.

Do you read "Nurone Abaro Anuranon" ?

Are u know about Euclid's theory about Prime Numbers are infinite ?

Not only you, many ''young mathematicians'' have made this mistake.(According to Md. Jafar Iqbal's 'তোমাদের প্রশ্ন আমার উত্তর')Euclid's proof has a second part.(It was not given in "Nurone Abaro Anuranon" for the sake of simplification)

This proof does not find a larger prime.Only confirms us that there exists such one.Notice that if $P_3$ and $P_4$ are not primes, Euclid's proof still works.Because then they must be composite.But they are dividable by none of all primes that we defined.So they must be dividable by a larger prime (let $P_m$) than our defined largest prime.Hence there exists a larger prime $P_m$ than our defined prime.But the existence of $P_m$ breaks your proof.

And an off topic mater : Tiham vaia is one of the most senior and genius campers.So you should think before saying he did not read kidding books like "Nurone Abaro Anuranon".