N 2 n 1 is prime
,This gives 2n+1=2a⋅2m+1. Now I suspect there's a way to factor that, but I don't see how. Can someone give me a hint? ,I'll try to recapituate all the comments made in an adapted version of the proof. If 2n−1 is prime from some integer n, then n must also be prime. Since the ... ,Hint: First, you'd need to know that (a−b)∣(an−bn) for all n∈N. Once you do that, consider the contrapositive (if n is not prime, then 2n−1 is not prime). ,2017年4月16日 — Proof 1: Factorising. Let n be even. Then n=2k for some k∈N. Hence 2n−1=22k−1=(2k−1)(2k+1). The edge case is n=4 (as this is the ... ,If 2n−1 is prime, then n cannot be 1. We show that n cannot be composite. Suppose to the contrary that n=ab, where a and b are greater than 1. ,2015年2月22日 — No, it's not. Among the first twenty thousand primes p, only thirty-one of them give primes when plugged into the formula ... ,Here we prove that if 2^n-1 is prime, then so is n. This is a key proof in understanding the Mersenne numbers. ,Mathematics says that a single example is enough to disprove a statement. Using this, put n=1 in the above statement which gives 1 as a result, which is not prime.
| 相關軟體 Write! 資訊 | |
|---|---|
 N 2 n 1 is prime 相關參考資料
Is $n^2 + n + 1$ prime for all n? - Mathematics Stack Exchange
https://math.stackexchange.com If $2^n+1$ is prime, why must $n$ be a power of $2 ...
This gives 2n+1=2a⋅2m+1. Now I suspect there's a way to factor that, but I don't see how. Can someone give me a hint? https://math.stackexchange.com If $2^n - 1$ is prime from some integer $n$, prove that n must ...
I'll try to recapituate all the comments made in an adapted version of the proof. If 2n−1 is prime from some integer n, then n must also be prime. Since the ... https://math.stackexchange.com Prove if, 2n−1 is prime, then n is prime. [duplicate] - Math ...
Hint: First, you'd need to know that (a−b)∣(an−bn) for all n∈N. Once you do that, consider the contrapositive (if n is not prime, then 2n−1 is not prime). https://math.stackexchange.com Showing $2^n -1$ is not prime for $n > 2$ where $n$ is even ...
2017年4月16日 — Proof 1: Factorising. Let n be even. Then n=2k for some k∈N. Hence 2n−1=22k−1=(2k−1)(2k+1). The edge case is n=4 (as this is the ... https://math.stackexchange.com Prove that if $2^n - 1$ is prime, then $n$ is prime for $n ...
If 2n−1 is prime, then n cannot be 1. We show that n cannot be composite. Suppose to the contrary that n=ab, where a and b are greater than 1. https://math.stackexchange.com Is it true that $2^n-1$ is prime whenever $n$ is prime ...
2015年2月22日 — No, it's not. Among the first twenty thousand primes p, only thirty-one of them give primes when plugged into the formula ... https://math.stackexchange.com If 2^n-1 is prime, then so is n - The Prime Pages
Here we prove that if 2^n-1 is prime, then so is n. This is a key proof in understanding the Mersenne numbers. https://primes.utm.edu n^2-n+1[math] always a prime number? - Quora
Mathematics says that a single example is enough to disprove a statement. Using this, put n=1 in the above statement which gives 1 as a result, which is not prime. https://www.quora.com |