Prime p₀= 2315713752103341101 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 46 2 40 2 136 2 22 2 (?)
a_n: 0 2 66 68 108 110 156 158 198 200 336 338 360 362
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: 362
Found by: Landjunge
db: batch=81, k=14, 64 40 46 40 136 22

SPT(16)	2315712752008326383	0 14 20 56 104 108 150 170 234 254 296 300 348 384 390 404	-1000095014718
SPT(13)	2315713057394822143	0 6 18 48 60 90 108 126 156 168 198 210 216	-694708518958
STPT(10)	2315713122663877619	0 2 12 14 90 92 168 170 180 182	-629439463482
SPT(16)	2315713327726593007	0 6 42 70 82 132 142 156 160 174 184 234 246 274 310 316	-424376748094
STPT(10)	2315713735107602309	0 2 18 20 30 32 42 44 60 62	-16995738792
SPT(16)	2315713744052549683	0 16 24 34 36 78 84 120 154 190 196 238 240 250 258 274	-8050791418
TPT(14)	2315713861673397611	0 2 30 32 60 62 108 110 180 182 240 242 306 308	109570056510
SPT(16)	2315713951281644779	0 28 54 154 202 208 210 288 334 412 414 420 468 568 594 622	199178303678
STPT(10)	2315714148496121039	0 2 18 20 30 32 42 44 60 62	396392779938
SPT(16)	2315714263094481247	0 34 70 76 144 150 154 166 180 192 196 202 270 276 312 346	510991140146
SPT(16)	2315714429293532693	0 18 20 24 48 54 74 138 200 264 284 290 314 318 320 338	677190191592