kaksospari

Kaksospari, known in English as twin primes, are pairs of prime numbers that differ by 2. Formally, a pair is (p, p+2) where both p and p+2 are prime. Examples include (3,5), (5,7), (11,13), (17,19), and (29,31).

A central open question is whether there are infinitely many kaksosparit. This is the twin prime conjecture, one of the longstanding unsolved problems in number theory. While extensive computational evidence confirms many instances of twin primes and various partial results constrain how primes can cluster, a proof of infinitude remains elusive.

If twin primes are infinite, their distribution is conjectured to follow the Hardy–Littlewood prime pair conjecture. The expected count of twin primes up to x is asymptotically about 2C2 ∫2^x dt/(ln t)^2, which is commonly approximated as 2C2 x/(ln x)^2 for large x. Here C2 is the twin prime constant, approximately 0.6601618, arising from correcting raw probabilistic estimates by considering correlations among primes modulo small primes.

Kaksospari are a specific case within the broader study of prime gaps and prime k-tuple conjectures. Related concepts include prime gaps, the distribution of primes, and the Hardy–Littlewood k-tuple conjecture, which generalizes the twin prime phenomenon to more complex constellations of primes.