The On-Line Encyclopedia of Integer Sequences lists the first ten prime quadruplets as {5, 7, 11, 13}, {11, 13, 17, 19}, {101, 103, 107, 109}, {191, 193, 197, 199}, {821, 823, 827, 829}, {1481, 1483, 1487, 1489}, {1871, 1873, 1877, 1879}, {2081, 2083, 2087, 2089}, {3251, 3253, 3257, 3259}, and {3461, 3463, 3467, 3469}.
If you want to find your own prime quadruplets, use the following sequence: {30n + 11, 30n + 13, 30n +17, 30n +19}, where n is an integer (though not every integer). To find new forms, start with a high number. The largest prime quadruplet known to mathematicians reaches over 2,058 digits, according to PrimeQuadruplet.co.tv.
Mathematicians debate on the finite nature of prime quadruplets; some believe that an infinite number of prime quadruplets exists, while others believe that prime quadruplets stop occurring at some unknown point.
By investigating prime quadruplets, mathematicians have discovered many patterns. For example, 733 prime quadruplets involving seven digit numbers exist, according to the University of Tennessee at Martin. Additionally, prime quadruplets are not the only form of prime constellation: mathematicians research prime pairs, prime triplets and even prime quintuplets.