Prime p₀= 819828759186293201 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 76 2 10 2 88 2 28 2 34 2 (?)
a_n: 0 2 120 122 198 200 210 212 300 302 330 332 366 368
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: 368
Found by: GLeeM
db: batch=73, k=14, 118 76 10 88 28 34

TPT(14)	819828076826118131	0 2 126 128 156 158 198 200 228 230 246 248 270 272	-682360175070
STPT(10)	819828082042754399	0 2 18 20 30 32 42 44 60 62	-677143538802
STPT(10)	819828270642551057	0 2 30 32 42 44 54 56 84 86	-488543742144
STPT(12)	819828354582016919	0 2 12 14 102 104 138 140 228 230 240 242	-404604276282
STPT(10)	819828531220129127	0 2 54 56 72 74 90 92 144 146	-227966164074
STPT(10)	819828643817798117	0 2 24 26 42 44 60 62 84 86	-115368495084
STPT(10)	819828810880598147	0 2 30 32 72 74 114 116 144 146	51694304946
STPT(10)	819828895867723097	0 2 30 32 72 74 114 116 144 146	136681429896
STPT(10)	819829005511590047	0 2 30 32 42 44 54 56 84 86	246325296846
SPT(16)	819829049091910103	0 26 74 126 158 168 210 228 236 254 296 306 338 390 438 464	289905616902
SPT(18)	819829074073123921	0 28 30 52 58 78 126 148 192 196 240 262 310 330 336 358 360 388	314886830720