More known initial prime k-tuplets ←

Oliver Atkin suggested that it would be of interest to record the smallest prime k-tuplet for each type of pattern.
In many cases it is trivial; for example, the two types of triplets are {5, 7, 11} and {7, 11, 13}.
(We exclude {3, 5, 7} because here all three residues modulo 3 are represented.)

With larger k it is not so easy. For instance, the smallest 20-tuplet of the pattern
{0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80} is
{29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109}.

However, before the discovery of a large prime 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski in October 2014,
there was no known example of the mirror-image pattern {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80}

Contributions to this section are welcome.

PRIME 17-TUPLETS

d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66
734975534793324512717947 ( 24 digits, 2009, Jörg Waldvogel )
753314125249587933791677 ( 24 digits, 2009, Jörg Waldvogel )
1341829940444122313597407 ( 25 digits, Jun 2021, Norman Luhn )

d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66
13
47624415490498763963983 ( 23 digits, 2001, Peter Leikauf and Jörg Waldvogel )
78314167738064529047713 ( 23 digits, 2001, Peter Leikauf and Jörg Waldvogel )
83405687980406998933663 ( 23 digits, 2001, Peter Leikauf and Jörg Waldvogel )
110885131130067570042703 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )
163027495131423420474913 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )

d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66
1620784518619319025971 ( 22 digits, 1997, Jörg Waldvogel )
2639154464612254121531 ( 22 digits, 1998, Jörg Waldvogel )
3259125690557440336631 ( 22 digits, 1998, Tony Forbes )
124211857692162527019731 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )

d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66
17
37630850994954402655487 ( 23 digits, 2001, Peter Leikauf and Jörg Waldvogel )
53947453971035573715707 ( 23 digits, 1998, Tony Forbes )
174856263959258260646207 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )
176964638100452596444067 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )
207068890313310815346497 ( 24 digits, Peter Leikauf and Jörg Waldvogel )
247620555224812786876877 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )
322237784423505559739147 ( 24 digits, 2001, Peter Leikauf and Jörg Waldvogel )

PRIME 18-TUPLETS

d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
2845372542509911868266807 ( 25 digits, 2000, Jörg Waldvogel & Peter Leikauf )
4530085223434265844952597 ( 25 digits, Dec 2008, Jaroslaw Wroblewski )

d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
13
1906230835046648293290043 ( 25 digits, 2001, Jörg Waldvogel & Peter Leikauf )

PRIME 19-TUPLETS

d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76
630134041802574490482213901 ( 27 digits, 9 Feb 2011, Raanan Chermoni & Jaroslaw Wroblewski )
656632460108426841186109951 ( 27 digits, 19 Feb 2011, Raanan Chermoni & Jaroslaw Wroblewski )

d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
37

d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76
smallest is unknown
...
622803914376064301858782434517 ( 30 digits, December 27, 2018, Raanan Chermoni & Jaroslaw Wroblewski )

d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76
13

PRIME 20-TUPLETS

d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80
29
3941119827895253385301920029 ( 28 digits, 24 June 2014, Raanan Chermoni & Jaroslaw Wroblewski )
38299233570943052294942174849 ( 29 digits, 9 Jan 2015, Raanan Chermoni & Jaroslaw Wroblewski )
39433867730216371575457664399 ( 29 digits, 8 Jan 2015, Raanan Chermoni & Jaroslaw Wroblewski )
97344384991448238094880899499 ( 29 digits, 11 Jul 2015, Raanan Chermoni & Jaroslaw Wroblewski )
111286948968140923889225384099 ( 30 digits, 12 Aug 2015, Raanan Chermoni & Jaroslaw Wroblewski )
121888742383899006588229597469 ( 30 digits, 9 Sep 2015, Raanan Chermoni & Jaroslaw Wroblewski )
131353007727172552185076031849 ( 30 digits, 8 Oct 2015, Raanan Chermoni & Jaroslaw Wroblewski )
138433730977092118055599751669 ( 30 digits, 8 Oct 2015, Raanan Chermoni & Jaroslaw Wroblewski )
140005104744811513908777956909 ( 30 digits, 8 Oct 2015, Raanan Chermoni & Jaroslaw Wroblewski )
140661282456312925227370009589 ( 30 digits, 8 Oct 2015, Raanan Chermoni & Jaroslaw Wroblewski )
248283957683772055928836513589 ( 30 digits, 1 Aug 2016, Raanan Chermoni & Jaroslaw Wroblewski )
260786413629117930695179308299 ( 30 digits, 7 Dec 2016, Raanan Chermoni & Jaroslaw Wroblewski )
320430661688896578454772807699 ( 30 digits, 24 May 2017, Raanan Chermoni & Jaroslaw Wroblewski )
349021296319127268299400177269 ( 30 digits, 24 May 2017, Raanan Chermoni & Jaroslaw Wroblewski )
452101241612347545944528242469 ( 30 digits, 28 Jan 2018, Raanan Chermoni & Jaroslaw Wroblewski )
494179332730633784520908832239 ( 30 digits, 23 May 2018, Raanan Chermoni & Jaroslaw Wroblewski )
562422394447827908154562532159 ( 30 digits, August 30, 2018, Raanan Chermoni & Jaroslaw Wroblewski )
593820854957327357933627374349 ( 30 digits, December 23, 2018, Raanan Chermoni & Jaroslaw Wroblewski )
594750459626903777773717631519 ( 30 digits, December 23, 2018, Raanan Chermoni & Jaroslaw Wroblewski )
639121700726230052098229452019 ( 30 digits, December 23, 2018, Raanan Chermoni & Jaroslaw Wroblewski )
701870455949526598513130862539 ( 30 digits, April 7, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
764364269069907627842423582909 ( 30 digits, July 17, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
789292095021856634277511882469 ( 30 digits, August 19, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
807462397198198801670343382679 ( 30 digits, September 25, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
831504454982803270879178298359 ( 30 digits, October 17, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
957278727962618711849051282459 ( 30 digits, March 23, 2020, Raanan Chermoni & Jaroslaw Wroblewski )
1094372814043722195189448411199 ( 31 digits, October 20, 2020, Raanan Chermoni & Jaroslaw Wroblewski )
1153897621507935436463788957529 ( 31 digits, December 26, 2020, Raanan Chermoni & Jaroslaw Wroblewski )
1188350591359110800209379560799 ( 31 digits, January 21, 2021, Raanan Chermoni & Jaroslaw Wroblewski )
1236637204227022808686214288579 ( 31 digits, May 23, 2021, Raanan Chermoni & Jaroslaw Wroblewski )

d = 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80
14374153072440029138813893241 ( 29 digits, October 6, 2014, Raanan Chermoni & Jaroslaw Wroblewski )
17546231261175189855273591491 ( 29 digits, 11 Dec 2014, Raanan Chermoni & Jaroslaw Wroblewski )
40814702190384518551961455541 ( 29 digits, 6 Feb, 2015, Raanan Chermoni & Jaroslaw Wroblewski )
58228410683159656922037124961 ( 29 digits, April 30, 2015, Raanan Chermoni & Jaroslaw Wroblewski )
69611500022230424427263424221 ( 29 digits, 22 Apr 2015, Raanan Chermoni & Jaroslaw Wroblewski )
114601431611676407654036210321 ( 30 digits, 3 Sep 2015, Raanan Chermoni & Jaroslaw Wroblewski )
131900255854906356663126180791 ( 30 digits, 20 Oct 2015, Raanan Chermoni & Jaroslaw Wroblewski )
154016910009801751265474541311 ( 30 digits, 16 Dec 2015, Raanan Chermoni & Jaroslaw Wroblewski )
161375347518710752668754312691 ( 30 digits, 3 Jan 2016, Raanan Chermoni & Jaroslaw Wroblewski )
182129285194786190875974840371 ( 30 digits, 16 Mar 2016, Raanan Chermoni & Jaroslaw Wroblewski )
185986500598659638316208079201 ( 30 digits, 16 Mar 2016, Raanan Chermoni & Jaroslaw Wroblewski )
187976201367296936422347098471 ( 30 digits, 16 Mar 2016, Raanan Chermoni & Jaroslaw Wroblewski )
220974232729147341120519932981 ( 30 digits, 31 May 2016, Raanan Chermoni & Jaroslaw Wroblewski )
227104691557231224024329351201 ( 30 digits, 1 Aug 2016, Raanan Chermoni & Jaroslaw Wroblewski )
242145669497919182306126385461 ( 30 digits, 1 Aug 2016, Raanan Chermoni & Jaroslaw Wroblewski )
352259532126245901475150592651 ( 30 digits, 24 May 2017, Raanan Chermoni & Jaroslaw Wroblewski )
400327605553593948618674105711 ( 30 digits, 7 Dec 2017, Raanan Chermoni & Jaroslaw Wroblewski )
403065917762608576939692599261 ( 30 digits, 7 Dec 2017, Raanan Chermoni & Jaroslaw Wroblewski )
466435879660522367654413675211 ( 30 digits, 15 Mar 2018, Raanan Chermoni & Jaroslaw Wroblewski )
562324418721793120042174985351 ( 30 digits, August 30, 2018, Raanan Chermoni & Jaroslaw Wroblewski )
622803914376064301858782434521 ( 30 digits, December 27, 2018, Raanan Chermoni & Jaroslaw Wroblewski )
667424014858149638371951648871 ( 30 digits, February 18, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
686962597479437604159786541481 ( 30 digits, April 27, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
839013472011818416634745523991 ( 30 digits, October 28, 2019, Raanan Chermoni & Jaroslaw Wroblewski )
999627565307688186459783232931 ( 30 digits, June 19, 2020, Raanan Chermoni & Jaroslaw Wroblewski )
1060475118776959297139870952701 ( 31 digits, September 18, 2020, Raanan Chermoni & Jaroslaw Wroblewski )
1126002593922465663847897293731 ( 31 digits, November 17, 2020, Raanan Chermoni & Jaroslaw Wroblewski )
1135540756371356698957890225821 ( 31 digits, December 19, 2020, Raanan Chermoni & Jaroslaw Wroblewski )

PRIME 21-TUPLETS

d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84
622803914376064301858782434517 ( 30 digits, December 27, 2018, Raanan Chermoni & Jaroslaw Wroblewski )

d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84
29
39433867730216371575457664399 ( 29 digits, 8 Jan 2015, Raanan Chermoni & Jaroslaw Wroblewski )
138433730977092118055599751669 ( 30 digits, 8 Oct 2015, Raanan Chermoni & Jaroslaw Wroblewski )
248283957683772055928836513589 ( 30 digits, 1 Aug 2016, Raanan Chermoni & Jaroslaw Wroblewski )