Prime p₀= 2667312210832666217 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 58 2 40 2 208 2 64 2 (?)
a_n: 0 2 30 32 72 74 132 134 174 176 384 386 450 452
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: 452
Found by: JayPi
db: batch=82, k=14, 28 40 58 40 208 64

SPT(16)	2667310860577406389	0 24 90 100 124 142 178 268 384 474 510 528 552 562 628 652	-1350255259828
SPT(16)	2667311508505711637	0 42 92 110 114 122 152 170 216 234 264 272 276 294 344 386	-702326954580
SPT(16)	2667311772147127057	0 30 54 66 112 124 156 162 184 190 222 234 280 292 316 346	-438685539160
STPT(10)	2667311777106364811	0 2 90 92 150 152 210 212 300 302	-433726301406
SPT(16)	2667312009889940923	0 4 30 48 100 124 130 138 160 168 174 198 250 268 294 298	-200942725294
SPT(16)	2667312171687457453	0 4 34 40 54 96 120 126 208 214 238 280 294 300 330 334	-39145208764
SPT(16)	2667312715544051093	0 24 74 80 126 134 164 176 318 330 360 368 414 420 470 494	504711384876
SPT(16)	2667313269694120147	0 42 46 52 60 72 84 90 196 202 214 226 234 240 244 286	1058861453930
TPT(14)	2667313375677246851	0 2 120 122 198 200 258 260 396 398 408 410 438 440	1164844580634
STPT(10)	2667313411030235249	0 2 42 44 60 62 78 80 120 122	1200197569032
STPT(10)	2667313418818115201	0 2 36 38 78 80 120 122 156 158	1207985448984