Prime p₀= 2136125348360122127 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 4 2 22 2 208 2 16 2 106 2 (?)
a_n: 0 2 24 26 30 32 54 56 264 266 282 284 390 392
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 392
Found by: Ben
db: batch=80, k=14, 22 4 22 208 16 106

SPT(16)	2136124135826266867	0 52 72 84 112 124 130 162 172 204 210 222 250 262 282 334	-1212533855260
TPT(14)	2136124617440712401	0 2 60 62 66 68 96 98 126 128 138 140 180 182	-730919409726
STPT(10)	2136124677694854599	0 2 18 20 30 32 42 44 60 62	-670665267528
TPT(14)	2136124841543220497	0 2 54 56 102 104 132 134 144 146 222 224 270 272	-506816901630
STPT(10)	2136125130858034397	0 2 54 56 72 74 90 92 144 146	-217502087730
STPT(10)	2136125332364333309	0 2 18 20 30 32 42 44 60 62	-15995788818
STPT(12)	2136125620312925567	0 2 30 32 42 44 132 134 144 146 174 176	271952803440
STPT(10)	2136125764326299561	0 2 6 8 48 50 90 92 96 98	415966177434
SPT(16)	2136126056040773963	0 18 48 74 90 104 108 168 200 260 264 278 294 320 350 368	707680651836
STPT(10)	2136126276212497991	0 2 36 38 78 80 120 122 156 158	927852375864
SPT(16)	2136126419938982617	0 40 42 60 70 76 100 112 144 156 180 186 196 214 216 256	1071578860490