- #1

evinda

Gold Member

MHB

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Hello! (Wave)

I am looking at the proof that $\prod_{p \leq 2n}p>2^n, \forall n \geq 2$, where the product extends over all primes $p \leq 2n$.

For $n<100$ the above proposition is shown as follows.

View attachment 7678

I was wondering if there is also an other way to prove the proposition for $n<100$.

Also is it a formal proof to just check that the proposition is true for some values $n<100$, as it is done at the picture above? (Thinking)

I am looking at the proof that $\prod_{p \leq 2n}p>2^n, \forall n \geq 2$, where the product extends over all primes $p \leq 2n$.

For $n<100$ the above proposition is shown as follows.

View attachment 7678

I was wondering if there is also an other way to prove the proposition for $n<100$.

Also is it a formal proof to just check that the proposition is true for some values $n<100$, as it is done at the picture above? (Thinking)