# Tagged Questions

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### Is there a prime number ending with the natural number $n$

if $n$ not is divisible by 2 or 5? Example: given 813075843967837637675737563754361301, there is a prime 20813075843967837637675737563754361301 or given ...
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### Prime number distribution theory for dummies

For the distribution of prime numbers there is a hypothesis which predicts the possible positions of prime numbers called Riemann hypothesis ...
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### Primes created by “n + digital-root(n)” sequences

I've looked at the sequences created by repeatedly adding the digital root of a number to the number until it becomes prime. This is the pseudo-code for the program I've used:   n = 0 ...
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### No primes in this sequence

Here's a fun little problem: Prove that the sequence $$10001, 100010001, 1000100010001, \cdots$$ contains no prime numbers.
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### Proof that $123456789098765432111$ is prime?

The mathematician Charles Weibel asks on his home page the following "fun question": How can you prove that 123456789098765432111 is a prime number? (He notes the fact 12345678987654321 = ...
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### Fictional math proof = prime return function

I am trying to write a piece of future fiction where one of the characters is famous for proving an important truth related to primes. I want to make it as realistic as possible, but i'm not a math ...
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### Find 7 digit prime numbers with this property;

When you subtract the sum of the squares of the digits of the number from the original number it gives you another prime number squared.
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### Is the number of alternating primes infinite?

I'm not sure if the recreational-mathematics tag is appropriate, but this problem came up during a practice Putnam seminar so maybe? The problem: Say that a positive integer is alternating if ...
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### The number of prime years in a lifetime

$2013$ is not a prime: $3 \times 11 \times 61$. I was born in a prime year, and if I live as expected according to the statistics for U.S. males, I will just reach another prime year, $2027$. That ...
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### Question about a program generating palindromic prime numbers

I'm a programmer and software designer. I'm definitely not a mathematician and my maths is quite basic. One of my colleagues challenged me to generate a palindromic prime number, at least 1000 digits ...
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### Super palindromes

Can anybody be kind enough to explain what exactly is a super palindrome? Also consider the following example : $923456781-123456789=799999992:9=88888888$ The largest prime factor of $88888888$ is ...
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### 9 hidden in every number regardless of number of digits?

Let us consider a number, e.g. 1234 Now reverse the positions of the terminal digits, so we get 4231 4231-1234=2997 which is divisible by 9 i have seen this for n-digit numbers, where n ranges ...
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### For which positive integers n does there exist a prime whose digits sum to n?

Motivated by this earlier question, I thought of this problem: Question: For which positive integers $n$ does there exist a prime whose decimal digits sum to $n$? We can make two "easy" ...
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### Is there an emirp greater than $10^{10006}+941992101 \times 10^{4999}+1$?

An emirp is a prime such that a distinct prime is formed when its digits are reversed. According to Wikipedia (and its references), the largest known emirp is \[p:=10^{10006}+941992101 \times ...
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### Flirtatious Primes

Here's a possibly interesting prime puzzle. Call a prime $p$ flirtatious if the sum of its digits is also prime. Are there finitely many flirtatious primes, or infinitely many?
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### Need a “Prime Square” type of number (For my significant other)

No this isn't for a silly math exercise, it's a relationship with a hottie I don't want to lose at stake: I like my TV volume to be on Perfect Squares, but she likes her volumes on Prime Numbers. ...
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### a big number that is obviously prime?

I once heard it asserted that $91$ is the smallest composite number that is not obviously composite. The reasoning was that any composite number divisible by $2$, $3$, or $5$ is obviously composite, ...
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### Always a prime between $x$ and $x+cf(x)$

What is the asymptotically slowest growing function $f(x)$, such that there exists constants $a$ and $b$, such that for all $x>a$, there is always a prime between $x$ and $x+bf(x)$? $f(x)=x$ ...
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### What is the millionth decimal digit of the (10^10^10^10)th prime?

What is the millionth decimal digit of the $10^{10^{10^{10}}}$th prime? (This prime is, of course, far larger than the largest currently "known" prime, the latter having nearly 13 million ...
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### $n$ by $n$ Primally Magic Squares

(Again copied verbatim from a September 2009 thread I made.) A Primally Magic Square (PMS) is exactly like a traditional magic square with a change of criteria. Where a traditional magic square is ...