Arithmetic progression of prime numbers

Thread starter sachinism
Start date Oct 2, 2010
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Arithmetic Arithmetic progression Numbers Prime Prime numbers

In summary, an arithmetic progression of prime numbers is a sequence where each number is obtained by adding a constant number to the previous number in the sequence. It must have a common difference, which distinguishes it from a regular sequence of prime numbers. Studying these progressions can help us better understand the distribution and properties of prime numbers. There is no known formula for generating them, but there are conjectures and theorems related to the topic. It is also possible for an arithmetic progression of prime numbers to have infinite terms, as proven by the existence of infinite arithmetic progressions of prime numbers.

Oct 2, 2010

sachinism

what is the maximum number of terms can a arithmetic progression of only prime numbers have?

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Oct 2, 2010

Petek

Gold Member

According to the Green-Tao Theorem, there is no such maximum.

Oct 2, 2010

sachinism

thanks a lot, that helped

1. What is an arithmetic progression of prime numbers?

An arithmetic progression of prime numbers is a sequence of prime numbers where each number is obtained by adding a constant number to the previous number in the sequence. For example, the sequence 5, 11, 17, 23 is an arithmetic progression of prime numbers with a common difference of 6.

2. Do all arithmetic progressions of prime numbers have a common difference?

Yes, by definition, an arithmetic progression of prime numbers must have a common difference. This is what distinguishes it from a regular sequence of prime numbers.

3. What is the importance of studying arithmetic progressions of prime numbers?

Studying arithmetic progressions of prime numbers can help us better understand the distribution of prime numbers, which is a fundamental problem in number theory. It can also provide insights into the properties and behavior of prime numbers.

4. Is there a formula for generating an arithmetic progression of prime numbers?

There is no known formula for generating an arithmetic progression of prime numbers. However, there are some conjectures and theorems related to this topic, such as the Green-Tao theorem which states that there are arithmetic progressions of prime numbers of any length.

5. Can an arithmetic progression of prime numbers contain infinite terms?

Yes, it is possible for an arithmetic progression of prime numbers to have infinite terms. This is known as an infinite arithmetic progression of prime numbers and it has been proven that there are infinitely many of them.