Prime p₀= 2105415972019443311 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 118 2 16 2 28 2 28 2 10 2 (?)
a_n: 0 2 60 62 180 182 198 200 228 230 258 260 270 272
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: Time_Traveler
db: batch=80, k=14, 58 118 16 28 28 10

STPT(10)	2105414895960567857	0 2 12 14 42 44 72 74 84 86	-1076058875454
TPT(14)	2105415036196105409	0 2 150 152 180 182 240 242 270 272 318 320 348 350	-935823337902
SPT(16)	2105415508838175997	0 24 40 52 100 130 162 172 204 214 246 276 324 336 352 376	-463181267314
SPT(16)	2105415603808549229	0 68 114 140 150 194 218 260 312 354 378 422 432 458 504 572	-368210894082
SPT(16)	2105415921517258447	0 10 12 54 60 94 96 100 126 130 132 166 172 214 216 226	-50502184864
STPT(10)	2105415954165720737	0 2 30 32 72 74 114 116 144 146	-17853722574
SPT(16)	2105416627609397293	0 16 28 34 46 60 126 130 144 148 214 228 240 246 258 274	655589953982
STPT(10)	2105416695071561489	0 2 48 50 60 62 72 74 120 122	723052118178
SPT(13)	2105416798792807183	0 60 66 126 150 204 210 216 270 294 354 360 420	826773363872
STPT(10)	2105416838412853541	0 2 36 38 78 80 120 122 156 158	866393410230
TPT(14)	2105416995668477597	0 2 54 56 84 86 210 212 264 266 372 374 390 392	1023649034286