Prime p₀= 2081572247886127697 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 4 2 82 2 46 2 16 2 70 2 (?)
a_n: 0 2 24 26 30 32 114 116 162 164 180 182 252 254
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: 254
Found by: Landjunge
db: batch=80, k=14, 22 4 82 46 16 70

SPT(16)	2081571717240526759	0 10 42 54 72 78 100 114 118 132 154 160 178 190 222 232	-530645600938
SPT(16)	2081571863623861529	0 30 32 44 60 90 104 110 174 180 194 224 240 252 254 284	-384262266168
SPT(16)	2081571886992594043	0 24 126 136 144 180 186 190 210 214 220 256 264 274 376 400	-360893533654
TPT(14)	2081571978404457899	0 2 120 122 138 140 150 152 252 254 330 332 390 392	-269481669798
SPT(16)	2081572158209554139	0 2 104 120 140 164 240 254 258 272 348 372 392 408 510 512	-89676573558
STPT(10)	2081572172558906009	0 2 12 14 90 92 168 170 180 182	-75327221688
SPT(16)	2081572867856038693	0 54 70 78 94 96 100 120 154 174 178 180 196 204 220 274	619969910996
SPT(16)	2081573038959217469	0 24 42 78 110 120 122 152 180 210 212 222 254 290 308 332	791073089772
SPT(16)	2081573079204952903	0 10 36 48 76 78 114 124 150 160 196 198 226 238 264 274	831318825206
SPT(16)	2081573377979513897	0 6 146 150 194 212 260 264 332 336 384 402 446 450 590 596	1130093386200
STPT(10)	2081573471840823731	0 2 78 80 138 140 198 200 276 278	1223954696034