One of the numbers n, n + 4, n + 8 will always be divisible by 3, so n = 3 is the only case where all three are primes.
An example of a large proven cousin prime pair is (p, p + 4) for which has 20008 digits.
As of December 2024[update], the largest-known pair of cousin primes was found by S. Batalov and has 86,138 digits.
An analogue of Brun's constant for twin primes can be defined for cousin primes, called Brun's constant for cousin primes, with the initial term (3, 7) omitted, by the convergent sum:[3] Using cousin primes up to 242, the value of B4 was estimated by Marek Wolf in 1996 as This constant should not be confused with Brun's constant for prime quadruplets, which is also denoted B4.
The Skewes number for cousin primes is 5206837 (Tóth (2019)).