Prime p₀= 2157135148819625789 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 34 2 28 2 10 2 88 2 10 2 (?)
a_n: 0 2 12 14 48 50 78 80 90 92 180 182 192 194
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: 194
Found by: Landjunge
db: batch=81, k=14, 10 34 28 10 88 10

TPT(14)	2157133105608867479	0 2 30 32 78 80 372 374 408 410 480 482 552 554	-2043210758310
STPT(10)	2157133345239317111	0 2 6 8 18 20 30 32 36 38	-1803580308678
STPT(12)	2157133360515415547	0 2 12 14 42 44 72 74 102 104 114 116	-1788304210242
SPT(16)	2157133429181315407	0 6 12 34 96 114 132 142 144 154 172 190 252 274 280 286	-1719638310382
SPT(16)	2157133813233841427	0 12 14 72 74 84 102 110 156 164 182 192 194 252 254 266	-1335585784362
SPT(16)	2157134503594817003	0 14 20 48 50 56 96 140 174 218 258 264 266 294 300 314	-645224808786
STPT(10)	2157135547552569641	0 2 36 38 78 80 120 122 156 158	398732943852
TPT(14)	2157135555256298597	0 2 54 56 192 194 210 212 324 326 390 392 402 404	406436672808
STPT(10)	2157135762310105277	0 2 30 32 42 44 54 56 84 86	613490479488
STPT(10)	2157135956362274747	0 2 30 32 72 74 114 116 144 146	807542648958
STPT(10)	2157136258048555967	0 2 30 32 42 44 54 56 84 86	1109228930178