Good prime

The term good prime is used in mathematics in different meanings. The common uses relate to the comparison of a prime with suitable averages of primes from the environment.

• 2.1 Examples

Definition by Erdős and Straus

The n- th prime number is called good if for all pairs of primes and, with from 1 to go, then:

It can be shown that there are infinitely many good primes. Are the first of which

This definition goes back to Paul Erdős and Ernst Gabor Straus.

Examples

It should be examined whether 11 is a good prime.

11 is the 5th prime number. So please check:

So, 11 is a good prime.

It should be examined whether 13 is a good prime.

13 is the 6th prime number. because

Does not apply. Therefore, 13 is not a good prime.

Attenuated definition

A prime number is good if it is greater than the geometric mean of the immediately adjacent pair of prime.

Thus, the n- th prime number is called good if

Also according to this definition, there are infinitely many prime numbers good denominated first of these

Examples

The 79 is in this sense a good prime, because

But it is not a good prime in the first sense, because is true for the previous primes