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Questions tagged [prime-numbers]

Prime numbers are natural numbers greater than 1 not divisible by any smaller number other than 1. This tag is intended for questions about, related to, or involving prime numbers.

A prime number (or a prime) is an element of the greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number ... The fundamental theorem of arithmetic establishes the central role of primes in :

Any integer greater than 1 can be expressed as a product of primes that is unique up to ordering.

Here you get the first 50 millions of primes.

The concept of prime numbers is extended in ring theory, where an element $p$ of a ring $R$ is prime if and only if whenever $p\mid ab$, then $p\mid a$ or $p\mid b$.

One can easily see that this extends the definition of prime numbers in the natural numbers.

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find positive prime number

Can anyone help on this? What is the positive integer such that the sum of the positive integer and 100 is a square number, and the sum of the positive integer and 168 is also a square number? Here is what I did: assume the positive integer being…
learning
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Partition of a prime $p$ into primes raised to a power to be dvisible by $p$

Find all the partitions of prime $p$ in primes less than $p$. Raise each term in each partition by some power $k > 1$ to see if the sum of these terms will be divisible by $p$. Of course, $k$ can differ for each partition. For example, for $5$, $2^3…
J. M. Bergot
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connection between two distinct prime numbers $p,q$ such that $p^n=q^2+q+1$

Let $p,q$ be two distinct prime number such that $p^n=q^2+q+1$, where $n \in \Bbb{N}$. I want to proof that, this forces $n=1$.
Rima
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Has anyone seen this Prime Pattern

I'm curious if anyone has noticed that all numbers that are primes must end in a 1, 3, 7, or 9, and that you can tell which ones don't by simply multiplying previous primes together and their exponents. So p*p & p^n will never be prime p*p always…
Durakken
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Is there a way to translate the Sacks Spiral into a triangle?

The sacks spiral is our natural number system written in the form of a spiral and it highlights the primes which seem to fall on certain curves within the spiral. I am interested to know if there is a way to translate the sacks spiral into a…
Joe
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is the multiplication of n consecutive prime numbers starting with 2 plus 1 prime?

The question kinda tell everything for itself, let P(n) be the n-th prime number, is $(\Pi_1^n P_n)+1$ prime ?
Ludovic Zenohate Lagouardette
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A question on Farey Sequences

We all know that Riemann Hypothesis (RH) has many equivalent statements. There is one statement which expresses RH in term of Redheffer matrix, there is another equivalent statement of RH which involves the Farey sequences. Are there similar…
david
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The Porsche prime

A friend told me that the number starting with 911 followed by 911 zeros ending with 119 (that is $911\cdot 10^{914}+119$) is a prime number, the so-called Porsche prime. Maple indeed confirms that this number is a prime. Does anybody know how this…
Joel Adler
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Find out if a number is prime

I read that every prime number is of the form $6k\pm1$, is this a correct approach to find out if a number is prime? auto isPrime = [&](int num) { if (num == 0 || num == 1) return false; if (num == 2 || num == 3) return…
Dean
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Prove amount of primes of form 4n-1 is infinite, looking for explanation of last part

This is an exercise in Bigg's Discrete Mathematics (Oxford Press). It is stated roughly like this: Suppose that there are finitely many primes of this form $(4n - 1): 3, 7, 11, 19,...,X$. Consider the number $$Y=4 \cdot…
Skurmedel
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Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$

What is given? $$\text{Let P be a prime}$$ $$\text{Let} \space f(x)= 3x+1$$ $$\text{Let} \space g(x)= 6x+1$$ Show that: If there exists $x \in \mathbb{N}$ such that $f(x) = P $ , then there exists a $y \in \mathbb{N}$ , such that $g(y) = P$ What…
Rubicon
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What is the percentage of prime numbers among all numbers with 100 decimal digits?

I know the Prime Number Theorem, but 100 digits numbers are too big to be put in a calculator. Is there a way of finding out how many primes numbers as a percentage of the total numbers with 100 decimal digits
chen
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find $x$ given arbitrary $\pi(x)$

When seeking the nth prime, how would one determine (or approximate) $x$, given a $\pi(x)$ value? I've read that $x / log(x)$ is a decent approximation of primes below $x$, but nothing about the reverse. I'm seeking an algorithm that can be easily…
JB0x2D1
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Primes from the given set

If we are given a set of positive integers and asked to find the prime numbers from this set considering the divisor must belong to this set only, Is there any way apart from dividing every number with other to do this. for e.g- the set…
Aryan
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A question about Prime Numbers (and its relation to RSA Asymmetric Cryptography)

Can someone kindly help me with the following question. Please bare in mind I am not good at maths, but I do get concepts, so I am looking to see if my current conceptual understanding is correct (rather than the math behind it) RSA Cryptography…
user2971567
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