Questions tagged [primes]
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Euclid's use of antenaresis and Heath's commentary
In Book 7, Prop. 1. Euclid uses repeated subtraction to prove that two numbers are relatively prime. As explained here the Greek word for repeated subtraction is "antenaresis". There isn't ...
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Autistic Assistant of Gauss used to check Primality
The Arora-Barak book on complexity contains the following sentence with the following footnote, page 128:
In primality testing, we are given an integer N and wish to determine
whether or not it is ...
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Simplest of the many proofs the prime harmonic series diverges
Over the history of mathematics, some key facts have had multiple and different proofs developed for them. Sometimes these different proofs provide a unique insight or understanding of those facts.
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$2^{11} - 1$ and the mystery of Huldaricus Regius
While researching on Mersenne numbers, I often stumble upon statements of this nature (it is not verbatim):
Huldaricus Regius in 1536 proved that $2^{11}-1$ is not prime, providing a factorisation ...
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Who discovered this closed form formula for the n-th prime number?
The following is a formula for the $n$-th prime number ($[\,]$ represents the floor function). Who was the first person to discover it?
$$\newcommand{\lowerbrack}[2]{%
\raise{-#1}{\left[\raise{#1}{#...
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First motivation for extending Riemann Zeta to complex domain?
Euler developed the Euler Product Formula which shows that the Riemann zeta function encodes information about the prime.
$$\zeta(s)=\sum_{n}\frac{1}{n^{s}}=\prod_{p}(1-\frac{1}{p^{s}})^{-1}$$
Riemann ...
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Was Cramér the first to interpret the PNT's $1/\log(x)$ as probability of primes?
The Cramér probabilistic model of primes is built on the assumption that the probability of $n$ being prime is
$$\Pr(n)=\frac{1}{\log (n)}$$
This is not a big leap from the Prime Number Theorem which ...
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Any historical work on the distribution of prime gaps?
I am looking to see whether historic mathematicians did any work to explain the slightly unexpected distribution of prime gaps?
I would have expected Gauss, who studied lists of primes and proposed a ...
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History of primality testing
Consider a uniform random variable $n$ which is an integer in the interval $2^{1023} < n < 2^{1024}$. What is the oldest algorithm capable of determining whether or not $p$ is a probable prime ...
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Euler's proof of infinite primes first since Euclid?
Q. Is it true that Euler's proof of infinite primes was the first since Euclid's which was from around 300BC?
Note: By Euler's proof, I mean the use of his Euler product formula for the zeta function ...
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