Prime p₀= 3022833052237456091 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 28 2 10 2 28 2 88 2 10 2 (?)
a_n: 0 2 96 98 126 128 138 140 168 170 258 260 270 272
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: 272
Found by: JayPi
db: batch=82, k=14, 94 28 10 28 88 10

SPT(16)	3022832026860816119	0 14 24 42 80 98 104 110 132 138 144 162 200 218 228 242	-1025376639972
STPT(12)	3022832144659782569	0 2 72 74 78 80 162 164 168 170 240 242	-907577673522
TPT(14)	3022832363142195911	0 2 108 110 126 128 138 140 156 158 180 182 240 242	-689095260180
STPT(10)	3022832466932452589	0 2 18 20 30 32 42 44 60 62	-585305003502
STPT(10)	3022832847673122257	0 2 42 44 72 74 102 104 144 146	-204564333834
STPT(10)	3022832959735477151	0 2 6 8 48 50 90 92 96 98	-92501978940
SPT(16)	3022833204441682207	0 4 10 34 76 90 120 186 220 286 316 330 372 396 402 406	152204226116
SPT(16)	3022833230977081289	0 8 42 78 102 108 228 252 260 284 404 410 434 470 504 512	178739625198
SPT(16)	3022833401307758771	0 42 62 80 140 152 188 192 218 222 258 270 330 348 368 410	349070302680
SPT(16)	3022833775593665651	0 2 18 30 62 78 120 128 132 140 182 198 230 242 258 260	723356209560
SPT(16)	3022834274176925501	0 18 42 68 86 126 152 170 198 216 242 282 300 326 350 368	1221939469410