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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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What is a distinct prime?

I need to know what a distinct prime is, and what happens when you multiply two of them. How can I figure this out?
SuperNinja741 Does Gaming
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What is the largest prime number?

I want to know, what is the largest prime number? I know prime numbers are whole numbers that cannot be divided by any whole number except 1 and themselves, I also know some primes like 2, 3, 5, 7, 11... But what is the largest prime number?
user151629
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How many consecutive prime numbers have been discovered?

Largest prime numbers discovered are continuously updated, however it is not clear how many consecutive prime numbers have been discovered. My question is : How many consecutive prime numbers have been discovered? In other words , what's the largest…
SacrificialEquation
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Prime numbers that are sums of Prime numbers themselves

what is the minimum prime number that is the sum of exactly two odd prime numbers? i.e I want to find a counter example to: $$p_i+p_j \in \mathbb P \operatorname{iff} i=1 \lor j=1$$
Adam Ledger
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If a number is not divisible by 2, 3 and 5, is enough to say that number is prime?

I'm Computer Science student. Last day, my teacher say this to the class room: "If a number is not divisible by 2, 3, and 5, mean that number is prime. This because odd numbers are divisible by 3 or 5, and even numbers by 2". That can be true? If…
Moige
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Number series problem

Find the missing number in the series ? $$6,49,305,?,6179,18560,37147$$
Prashant Mathur
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What is the significance of infinite number of primes?

What caused Euclid and Euler to prove this theorem?
Shivam Kumar
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Regarding one form of potential primes

If we think of primes of the form $a^n-b^n,$ where $a,b,n$ are positive natural numbers and $a>b$, $(a-b)\mid (a^n-b^n)$, so $a-b$ must be $1$ and $n$ must be prime else $(a^r-b^r)\mid (a^n-b^n)$ where $r>1$ and $r\mid n$ So, $a^n-b^n$ reduces to…
lab bhattacharjee
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Could somebody prove that there are infinite values of a and b where both 6a-1 and 12b-1 are prime?

By asking this question, I hope that someone, somewhere, has an answer, not to the conjecture, but the question itself. Then, that person has proved an unsolved conjecture. I do have a proof, which is quite long, that all Germain primes are of the…
mngi
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Is the largest prime number known? If yes then show. If no then prove.

I am not sure whether is known or not, I supposed not but don'nt know how to prove.
Surdz
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How can I prove or disprove that the formula $2^{2{^{2^{2^2\dots}}}}+1$ gives a prime number?

I could calculate the following $$2+1=3$$ $$2^2+1=5$$ $$2^{2^2}+1=17$$ $$2^{2{^{2^2}}}+1=65537$$ Now how can I prove or disprove the formula always gives a prime number
E.H.E
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What are the consequences of revealing pattern in prime numbers?

I have been studying structure of numbers and came across a unique property of prime numbers. I would be happy to share my discovery, which would help, for example, in understanding Goldbach's conjecture. On the other hand the pattern I see could be…
LAAE
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Weird Prime Number Discovery

I noticed a strange phenomenon while examining prime numbers. Here it is: We'll say num = number If num's sum of digits is 4 and num is not even, num is prime. Can somebody explain to me why this happens? Here is a Node.js program for proof:…
TigerGold
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