can a number be both prime and irrational?

Question

help!

Answer 1

No its not possible...

Irrational numbers has no ending, & they have lots of decimal places. So concept of primes is not there..

If any number is a prime it MUST be an integer which I dont think any irrational number can satisfy that.. :)

Regards,
Codered

Answer 2

For the second time today: no. Prime numbers must be, by definition, integers. An irrational number can't be an integer, because all integers are rational numbers.

Granted, you can get into some higher levels of math where "prime" is used to describe certain things other than prime numbers (integers), but that's just confusing the matter unnecessarily. When we talk about a number being "prime", it's safe to assume we're talking about the classic subject of integers with no integer factors other than 1 and themselves.

Answer 3

Not until you get to college-level advanced math (such as number theory). The previous posters are generally correct: the classic prime numbers are integers, and every integer is a rational number.

However, there are things called "Gaussian primes", working with sets of numbers of the form J+K*sqrt(N), usually for a specific value of N (N, J, and K are integers). As with the classic (integral) primes, one of these numbers is a "prime" of the set iff it has no non-tricial divisors. For instance, given the family based on sqrt(3), is the integer 2 a prime? No: it's the product of sqrt(3)+1 and sqrt(3)-1, each of which *is* a prime in the set.

There are also Gaussian primes over the complex numbers (those involving *i*, sqrt(-1)). The definition of "prime" works the same way. Note that 2 is also not a prime in the complex numbers, as it's (1+i)*(1-i).

Answer 4

No. Primes are a subset of integers, and integers a subset of rational numbers. Rational numbers and irrational numbers are two mutually exclusive sets. Thus, primes and irrational numbers are mutually exclusive, making it so that a number CANNOT be both prime and irrational.

Answer 5

Generally by "prime" we mean a whole number that has only itself and 1 as whole number factors. Since all primes are whole numbers, and all whole numbers are rational, therre cannot be any prime irrational numbers, in the usual sense of these words. However, there are other kinds of primes, such as Gaussian Primes and prime polynomials. See...
Gaussian Primes
http://mathworld.wolfram.com/GaussianPrime.html
prime polynomials
http://en.wikipedia.org/wiki/Irreducible_polynomial

Answer 6

Not if you are talking about whole number primes because.
every whole number is rational.
But if you are talking about, say, Gaussian
primes, then the answer is yes.
1+i is a Gaussian prime and is irrational as well.
It depends on the base ring we are looking at.

Answer 7

No. Irrational numbers are numbers that can't be expressed as fractions (they go on without repeating themselves, like pi). Prime numbers are integers, so they can be expressed as fractions.

Answer 8

The concept of prime numbers is applied normally only to natural integers but never to irrationals.
Gauss extended it to complex numbers but I think that this is not
your scope.

Answer 9

No. Only integers are prime numbers, and integers are all rational.

Edit: I get all these thumbs down for stating a simple mathematical definition?? Jeez, tough crowd.

Answer 10

No, because only integers can be prime, but all integers are rational.