Tagged Questions

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.

20k views

Is $7$ the only prime followed by a cube?

I discovered this site which claims that "$7$ is the only prime followed by a cube". I find this statement rather surprising. Is this true? Where might I find a proof that shows this? In my ...
25k views

Deleting any digit yields a prime… is there a name for this?

My son likes his grilled cheese sandwich cut into various numbers, the number depends on his mood. His mother won't indulge his requests, but I often will. Here is the day he wanted 100: But ...
13k views

What is the Riemann-Zeta function?

In laymen's terms, as much as possible: What is the Riemann-Zeta function, and why does it come up so often with relation to prime numbers?
9k views

Infiniteness of non-twin primes.

Well, we all know the twin prime conjecture. There are infinitely many primes $p$, such that $p+2$ is also prime. Well, I actually got asked in a discrete mathematics course, to prove that there are ...
3k views

Least prime of the form $38^n+31$

I search the least n such that $$38^n+31$$ is prime. I checked the $n$ upto $3000$ and found none, so the least prime of that form must have more than $4000$ digits. I am content with a probable ...
4k views

7k views

The myth of no prime formula?

Terence Tao claims: For instance, we have an exact formula for the $n^\text{th}$ square number – it is $n^2$ – but we do not have a (useful) exact formula for the $n^\text{th}$ ...
1k views

Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers?

Our algebra teacher usually gives us a paper of $20-30$ questions for our homework. But each week, he tells us to do all the questions which their number is on a specific form. For example, last ...
13k views

Why is Euclid's proof on the infinitude of primes considered a proof?

I've expressed Euclid's proof on the infinitude of primes on Mathematica: ...
6k views

Are there an infinite number of prime numbers where removing any number of digits leaves a prime?

Suppose for the purpose of this question that number $1$ is a prime number. Consider the prime number $311$. If we remove one $1$ from the number we arrive at the number $31$ which is also prime. If ...
4k views

How did Euler prove the Mersenne number $2^{31}-1$ is a prime so early in history?

I read that Euler proved $2^{31} -1$ is prime. What techniques did he use to prove this so early on in history? Isn't very large number stuff done with computers? Do you know if Euler had a team of ...
1k views

Mathematicians shocked(?) to find pattern in prime numbers

There is an interesting recent article "Mathematicians shocked to find pattern in "random" prime numbers" in New Scientist. (Don't you love math titles in the popular press? Compare to the source ...
3k views

$5^n+n$ is never prime?

In the comments to the question: If $(a^{n}+n ) \mid (b^{n}+n)$ for all $n$, then $a=b$, there was a claim that $5^n+n$ is never prime (for integer $n>0$). It does not look obvious to prove, nor ...
5k views

Is this of any real importance to the mathematical scientific community?

I'm a 31 year old engineer, and I've recently came up with a way to exactly predict the probability of the number of prime numbers between two different integers. For example using my way, the number ...
3k views

Does the string of prime numbers contain all natural numbers?

Does the string of prime numbers $$2357111317\ldots$$ contain every natural number as its sub-string?
17k views

For any prime $p > 3$, why is $p^2-1$ always divisible by 24?

I know this is very basic and old hat to many, but I love this question and I am interested in seeing whether there are any proofs beyond the two I already know.
7k views

Why are primes considered to be the “building blocks” of the integers?

I watched the video of Terence Tao on Stephen Colbert the other day (here), and he stated, like many mathematicians do, that the primes are the building blocks of the integers. I've always had ...
5k views

Does every prime divide some Fibonacci number?

I am tring to show that $\forall a \in \Bbb P\; \exists n\in\Bbb N : a|F_n$, where $F$ is the fibonacci sequence defined as $\{F_n\}:F_0 = 0, F_1 = 1, F_n = F_{n-1} + F_{n-2}$ $(n=2,3,...)$. How can ...
4k views

Eyebrow-raising pattern of number of primes between terms of the Fibonacci number sequence?

So, $$1,1,2,3,5,8,13,21...$$ Any connection to primes?...it appears not. However, in between the Fibonacci numbers are how much primes? Let's see: 1 and 1 ZERO 1 and 2 NADA 2 and 3 ZILCH 3 and 5 ZIP ...