# 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.

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### An interesting algorithm about prime numbers that I thought today

I thought up the following algorithm today: Choose $a_1\in\mathbb{Z}^+\setminus\{1\}$. Then let $a_{n+1}=a_n+p_n$, where $p_n$ is the largest prime factor of $a_n$. The algorithm is easy, but I ...
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### Prime number and Relationship of Sequences of period 4,5,and 6

Let $p$ be a prime number.($p \neq 2,3,5$) Let $t^+,t^-,a$ be sequences. $t^+_{k+5}=t^+_k,t^+_1=0,t^+_2=-1,t^+_3=-1,t^+_4=0,t^+_5=2$ $t^-_{k+5}=t^-_k,t^-_1=-1,t^-_2=0,t^-_3=0,t^-_4=-1,t^-_5=2$ \$a_k=...
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### Can we remove any prime number from this strange process?

This is a little algorithm I made today, which may appear to be quite complex, so I will start with an example. Questions are at the end of the post. The process goes as follows: Start with the ...