28 questions linked to/from Why is $1$ not a prime number?
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### Should we or should we not take $1$ as a prime number? [duplicate]

I think I know that there were times in the past when it was convenient to look at a number $1$ as a prime number, and, as far as I can remember, even then it was dependent on who we ask is it prime ...
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### Why 1 is not prime [duplicate]

I have been told that there is some interesting mathematics to why the number 1 is not prime. Can someone explain why one is not a prime number?
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### Why $1$ isn't a prime? [duplicate]

I was wondering the reason behind defining the Prime Numbers in a manner of which $1$ isn't an example. I read in Rotman's A First Course in Abstract Algebra that one reason that $1$ is not called a ...
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### Why was 1 considered as prime years ago? [duplicate]

I've seen on Maths Is Fun that years ago, 1 was considered as prime, but now, it is not. How did this happen? I know that a prime number has only two factors, 1 and itself, and we have 1, which is ...
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### What will accepting 1 as prime change? [duplicate]

How significant is the fact 1 isn't a prime number? What will happen if it is? What areas of Mathematics are affected by changing the fact? I know why and how 1 isn't a prime. My question is how ...
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### Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?

I know that $1$ is not a prime number because $1\cdot\mathbb Z=\mathbb Z$ is, by convention, not a prime ideal in the ring $\mathbb Z$. However, since $\mathbb Z$ is a domain, $0\cdot\mathbb Z=0$ is ...
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### Why is two to the power of zero equal to binary one?

Probably a simple question and possibly not asked very well. What I want to know is.. In binary, a decimal value of 1 is also 1. It can be expressed as $x = 1 \times 2^0$ Question: Why is two to ...
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### Is every positive nonprime number at equal distance between two prime numbers?

For example $8$ is in the middle of the interval between $5$ and $11$, $9$ is at equal distance between $7$ and $11$; $10$ between $7$ and $13$.
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### What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?

The title pretty much says it all. Of course, one answer (IMO unsatisfactory) to such questions goes something like "a definition is a definition, period." In my experience, mathematical definitions ...
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### Why do we call primes, and not the number one, *the atoms of numbers*?

The fundamental theorem of arithmetic asserts that we can produce every composite number from a unique set of prime multiplicands, so long as none of those primes equals one. Consequently, some ...
Okay, so almost 3 months into my abstract algebra, we just started rings. I have a few questions. A "trivial ring" is a ring with only one element. So $R={0}$ is a trivial ring. Understandable. ...
### Commutative ring $R$ such that $R[x]$ has nonconstant units.
I have an exercise asking to give an example of a commutative ring $R$ such that $R[x]$ has nonconstant units. At first glance, surely $\mathbb{Z}[x]$ is a commutative ring and would give nonconstant ...