1
vote
1answer
21 views

Probability Distribution of Count of Factors for All Numbers

Is the following a known thing? Define "factor count" as the count of factors each number has, then subtract 1. Ignore the number "1" as a factor. For example: Prime numbers have a factor count ...
3
votes
5answers
202 views

Product of all primes

Is the product of all primes a natural number? In other words, is this true: $$ \prod\limits_{\text{primes}} p_i \in \mathbb{N} $$ And if so, what about just some of them: $$ ...
1
vote
1answer
131 views

Why prime number theorem tends to one

I am curious about prime numbers so i just started reading about it. While reading some articles i came across prime number therom (PMT) which states like this $\displaystyle \lim_{n \to \infty} \pi ...
16
votes
2answers
613 views

Is there an infinite number of primes constructed as in Euclid's proof?

In Euclid's proof that there are infinitely many primes, the number $p_1 p_2 ... p_n + 1$ is constructed and proved to be either a prime, or a product of primes greater than $p_n$. Trivially, we ...
6
votes
2answers
568 views

Infinite Prime Proof Using Euler's Totient

I need something explained or corrected: In my number theory class we proved that there are an infinite number of primes using Euler's Phi Totient. It went something like this: Let $M = p_1 p_2 ...