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Hello everybody,

It seems generally admitted that there are no negative prime numbers.

What are the rules that can affirm this?

Thanks in advance and happy new year to all.

Best regards,

It seems generally admitted that there are no negative prime numbers.

What are the rules that can affirm this?

Thanks in advance and happy new year to all.

Best regards,

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Wikipedia said :

In this case, why it would be wrong to said that "

If we follow this common rule, this number is then divisible by 1 (positive) and of course itself (negative).

Is this correct ?

for the equations:

```
-585968374389626759 / 1 = -585968374389626759
-585968374389626759 / -585968374389626759 = 1
```

these is correct to prove that the big number can be divisible by 1 and by itself.some other discussions can be found here:

https://math.stackexchange.com/questions/1002459/do-we-have-negative-prime-numbers

one interesting note is that if a prime number like: -7 can be considered as a prime number, but in the fact it's divisible by -1 and 7, and then 1 and -7.

This is true that we can't check this same negative value on those websites.

Just have a look to our online tool that make it possible check negative prime numbers.

Do you think we made a mistake ?

Thanks in advance .. ... .....

In this case, why it would be wrong to said that "-585968374389626759" is a prime number ?Simply by definition.

Cause -585968374389626759 is NOT a natural number. Thus the prime number rules does not apply.

And now it's getting to be fun: You can generalize this idea. But then this is called prime element..

It also fails the "no positive divisors other..." on two counts. -585968374389626759 is not a positive divisor so that isn't part of "1 and itself". It does have a second positive divisor, namely 585968374389626759, but that is neither 1 nor itself.

In simple terms, if 2 is prime, then so is -2. So 4 (the smallest composite number) no longer has a unique factorization. In fact, no composite number will have a unique factorization.

This would do enormous damage to Number Theory with no discernible benefit.

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Start your 7-day free trialSo, finally, a prime number seems to be prime not because of its own intrasecs properties, but

In this case, how to name all negative numbers mirrors to positive prime numbers that have the same values?

Is there a category for classifying these "

Thank you for your reply and see you soon ... ... .....

Best regards,

I think you'll have to come up with a specific definition for this before it can be answered.

Depending on how you define "negative prime numbers" I would expect that there are none or there are exactly as many as prime numbers.

For example, 3 is prime. -3 has 4 divisors: (+-1 and +-3). If you eliminate the explicit restriction on primes being positive, negatives of prime numbers won't be prime as they'll have 4 divisors. You could define them as "numbers that have only four divisors, positive and negative one and the positive and negative value of themselves", but what would be the point?

As d-glitch mentioned, this could well have far-reaching impact in other parts of Number Theory.

You make a reference to "intrinsic properties" of numbers. I'm not sure that numbers have ANY intrinsic properties other than what arise from what we define. 0 and 1 may be exceptions to that, but I'm not even sure there.

In this case, how to name all negative numbers mirrors to positive prime numbers that have the same values?You can name them exactly like that. Mirrors.

Is there a category for classifying these "negative prime numbers"?Afaik no. Cause the only generalization of prime numbers I know are prime elements, which require a (algebraic) ring. Z (all integers, positive, 0 and negative) form a ring, but primes require only one unit. Your approach over Z requires two. So strictly speaking, they are not "primes".

So CompProbSolv is right. Your definition maybe useful in your use-case, but in general terms this defintion has draw backs like violating the Fundamental Theorem.

prime numbers

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Prime number

https://en.wikipedia.org/wiki/Prime_number