Prime p₀= 2081113910260272707 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 16 2 130 2 34 2 10 2 10 2 (?)
a_n: 0 2 54 56 72 74 204 206 240 242 252 254 264 266
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: 266
Found by: MarkRBright
db: batch=80, k=14, 52 16 130 34 10 10

SPT(16)	2081112743935929427	0 54 72 84 94 136 150 166 180 196 210 252 262 274 292 346	-1166324343280
SPT(16)	2081112878814956423	0 6 24 38 50 90 104 120 194 210 224 264 276 290 308 314	-1031445316284
SPT(16)	2081112884360978861	0 8 42 156 162 182 198 222 266 290 306 326 332 446 480 488	-1025899293846
SPT(16)	2081112929393675159	0 90 104 114 138 140 164 198 230 264 288 290 314 324 338 428	-980866597548
STPT(10)	2081113581098280299	0 2 18 20 30 32 42 44 60 62	-329161992408
STPT(10)	2081113865606988761	0 2 6 8 48 50 90 92 96 98	-44653283946
SPT(16)	2081114238609265711	0 60 82 96 102 118 120 148 150 178 180 196 202 216 238 298	328348993004
STPT(10)	2081114288926528379	0 2 18 20 30 32 42 44 60 62	378666255672
STPT(10)	2081114665284037307	0 2 12 14 42 44 72 74 84 86	755023764600
STPT(10)	2081115363566019617	0 2 12 14 72 74 132 134 144 146	1453305746910
TPT(14)	2081115559156690751	0 2 6 8 60 62 90 92 168 170 300 302 336 338	1648896418044