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Sexy Primes (two primes separated by 6)

Sexy primes are two primes separated by 6. This can be extended to sexy triplets and sexy quadruplets, but not further due to divisibility by 5 - apart from the single non-consecutive quintuplet (5, 11, 17, 23, 29). The definition does not require consecutive primes but the records have it. The below table shows the record history since 2010.

The largest known sexy CPAP's
k Primes n's Digits Year Discoverer(s)
3
2494779036241 249800+ 1 + 6n n=0..2 15004 2022 Serge Batalov
3
3428602715439 235678 + 1 + 6n n=0..2 10753 2020 Serge Batalov
3
2683143625525 235176 + 1 + 6n n=0..2 10602 2019 Gerd Lamprecht & Norman Luhn APSieve, Primo
3
18416522281203 233222 - 1 + 6n n=0..2 10015 2020 Peter Kaiser, Primo
3
22582235875 222224 + 1 + 6n n=0..2 6701 2019 Norman Luhn & Gerd Lamprecht, APSieve, Primo
3 (72865897 809857 4801# (809857 4801# + 1) + 210) (809857 4801# - 1) / 35 + 1 + 6n n=0..2 6180 2019 Ken Davis, PrimeForm, APTreeSieve
3
20730011943 14221# + 344231 + 6n n=0..2 6116 2019 Gerd Lamprecht, APSieve, PrimeForm, Primo
3
10409207693 220000 - 1 + 6n n=0..2 6031
2019 Peter Kaiser
3
12909901425 12391# + 344237 + 6n n=0..2 5320 2018 Gerd Lamprecht, APSieve, PrimeForm, Primo
3 (84055657369 205881 4001# (205881 4001# + 1) + 210) (205881 4001# - 1) / 35 + 1 + 6n n=0..2 5132 2006 Ken Davis, PrimeForm, APTreeSieve

4 121152729080 7019# / 1729 + 1 + 6n n=0..3 3025 2019 Gerd Lamprecht & Norman Luhn, PrimeForm, Primo
4 1901870849 (269504 1601# (269504 1601# + 1) (269504 1601# - 1) / 385) + 6 (269504 1601# - 1) - 5 + 6n n=0..3 2053 2019 Ken Davis, APTreeSieve, PrimeForm, Primo
4 46329193156 4657# + 344231 + 6n n=0..3 2001 2019 Gerd Lamprecht, Primo
4 19299420002127 25050 + 17233 + 6n n=0..3 1534 2019 Peter Kaiser, PrimeForm, Primo
4 1567237911 2677# + 3301 + 6n n=0..3 1138 2019 Marek Hubal, PrimeForm, Primo
4 37675946750 2400# + 344231 + 6n n=0..3 1034 2018 Gerd Lamprecht, APSieve, PrimeForm, Primo
4 23333 + 1582534968299 + 6n n=0..3 1004 2010 Ken Davis, PrimeForm, Primo