It is not known if there are infinitely many prime quadruplets.

A prime quadruplet of this form is also called a prime decade.

There is also a Brun's constant for prime quadruplets.

This constant should not be confused with Brun's constant for prime quadruplets, which is also denoted B.

A prime quadruplet contains two pairs of twin primes and two overlapping prime triplets.

A prime quadruplet is a pair of two twin prime pairs, separated by a distance of 4 (the smallest possible distance).

Also, proving that there are infinitely many prime quadruplets might not necessarily prove that there are infinitely many prime quintuplets.

Brun's constant for prime quadruplets, denoted by B, is the sum of the reciprocals of all prime quadruplets:

Professor Thomas Nicely, a professor of mathematics at Lynchburg College, had written code to enumerate primes, twin primes, prime triplets, and prime quadruplets.

A proof that there are infinitely many would imply the twin prime conjecture, but it is consistent with current knowledge that there may be infinitely many pairs of twin primes and only finitely many prime quadruplets.