Prime Triplet Conjecture

Conjecture

It is conjectured that there exist infinitely many prime triplets: that is, sets of three (positive) prime numbers either:

$\set {n, n + 2, n + 6}$

or:

$\set {n, n + 4, n + 6}$.

Historical Note

Hardy (we presume) announces the following in $1938$ or thereabouts:

Such conjectures, with larger sets of primes, may be multiplied, but their proof or disproof is at present beyond the resources of mathematicians.

Research into this subject is ongoing at time of writing in the early $2020$'s, and greatly aided by the efforts of silicon-based lifeforms.

Sources

• 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.) ... (previous) ... (next): $\text I$: The Series of Primes: $1.4$ The sequence of primes