Prime p₀= 2309688225177865421 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 58 2 70 2 46 2 70 2 16 2 (?)
a_n: 0 2 108 110 168 170 240 242 288 290 360 362 378 380
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: 380
Found by: FritzB
db: batch=81, k=14, 106 58 70 46 70 16

SPT(16)	2309686821400004591	0 12 30 32 122 128 140 150 158 168 180 186 276 278 296 308	-1403777860830
STPT(10)	2309687384188426127	0 2 54 56 72 74 90 92 144 146	-840989439294
TPT(14)	2309688067967779727	0 2 42 44 114 116 132 134 174 176 252 254 282 284	-157210085694
TPT(14)	2309688112836422957	0 2 60 62 72 74 84 86 90 92 132 134 174 176	-112341442464
STPT(10)	2309688113082811157	0 2 54 56 72 74 90 92 144 146	-112095054264
SPT(16)	2309688175676327879	0 12 42 44 54 132 158 168 284 294 320 398 408 410 440 452	-49501537542
SPT(16)	2309688267601842389	0 38 54 62 104 108 110 132 140 162 164 168 210 218 234 272	42423976968
STPT(10)	2309688405395307017	0 2 42 44 72 74 102 104 144 146	180217441596
SPT(16)	2309688466057968907	0 22 42 64 130 132 150 172 174 196 214 216 282 304 324 346	240880103486
SPT(16)	2309689026608270429	0 2 20 24 78 90 122 140 162 180 212 224 278 282 300 302	801430405008
STPT(10)	2309689383668835977	0 2 12 14 42 44 72 74 84 86	1158490970556