Prime p₀= 2157082958199821609 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 34 2 40 2 16 2 (?)
a_n: 0 2 60 62 72 74 102 104 138 140 180 182 198 200
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: 200
Found by: Landjunge
db: batch=81, k=14, 58 10 28 34 40 16

SPT(16)	2157081893066435801	0 6 26 56 98 102 126 138 140 152 176 180 222 252 272 278	-1065133385808
STPT(10)	2157081965298179327	0 2 42 44 72 74 102 104 144 146	-992901642282
SPT(16)	2157082008546407321	0 2 12 32 42 78 108 122 198 212 242 278 288 308 318 320	-949653414288
TPT(14)	2157082315993225667	0 2 54 56 60 62 90 92 114 116 144 146 180 182	-642206595942
SPT(16)	2157082540586783401	0 16 22 30 88 132 160 168 190 198 226 270 328 336 342 358	-417613038208
STPT(10)	2157082638182510567	0 2 60 62 72 74 84 86 144 146	-320017311042
SPT(16)	2157083181994527317	0 20 42 56 62 72 102 104 192 194 224 234 240 254 276 296	223794705708
TPT(14)	2157083638914049511	0 2 66 68 96 98 156 158 276 278 378 380 420 422	680714227902
TPT(14)	2157083647480732757	0 2 12 14 24 26 90 92 132 134 150 152 210 212	689280911148
SPT(16)	2157083706801081277	0 16 46 60 72 102 114 142 174 202 214 244 256 270 300 316	748601259668
STPT(10)	2157083750347334927	0 2 24 26 42 44 60 62 84 86	792147513318