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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