Prime p₀= 2309702788290010667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 16 2 88 2 40 2 4 2 (?)
a_n: 0 2 30 32 54 56 72 74 162 164 204 206 210 212
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: 212
Found by: FritzB
db: batch=81, k=14, 28 22 16 88 40 4

TPT(14)	2309702394623912831	0 2 30 32 48 50 168 170 210 212 228 230 240 242	-393666097836
SPT(16)	2309702443153204529	0 48 62 110 122 134 162 222 260 320 348 360 372 420 434 482	-345136806138
SPT(16)	2309702513813681773	0 76 78 106 174 208 216 220 264 268 276 310 378 406 408 484	-274476328894
STPT(10)	2309702523245566451	0 2 30 32 60 62 90 92 120 122	-265044444216
SPT(16)	2309702709022498661	0 42 60 62 68 72 86 102 266 282 296 300 306 308 326 368	-79267512006
STPT(10)	2309702759994434471	0 2 6 8 18 20 30 32 36 38	-28295576196
TPT(14)	2309703359403152849	0 2 12 14 42 44 48 50 120 122 132 134 180 182	571113142182
SPT(16)	2309703476975354557	0 6 16 40 60 82 96 100 126 130 144 166 186 210 220 226	688685343890
STPT(10)	2309703808058521487	0 2 30 32 42 44 54 56 84 86	1019768510820
STPT(10)	2309703817831040987	0 2 30 32 72 74 114 116 144 146	1029541030320
SPT(16)	2309704075031357231	0 6 36 42 50 90 120 152 156 188 218 258 266 272 302 308	1286741346564