Prime p₀= 916817308788008039 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 166 2 82 2 28 2 76 2 28 2 16 2 (?)
a_n: 0 2 168 170 252 254 282 284 360 362 390 392 408 410
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: 410
Found by: Theadalus
db: batch=76, k=14, 166 82 28 76 28 16

SPT(16)	916815990870509011	0 22 28 58 72 78 88 90 100 102 112 118 132 162 168 190	-1317917499028
STPT(10)	916816264988607017	0 2 60 62 72 74 84 86 144 146	-1043799401022
STPT(10)	916816273009491467	0 2 30 32 42 44 54 56 84 86	-1035778516572
SPT(18)	916816500700996967	0 42 102 122 126 140 152 180 192 194 206 234 246 260 264 284 344 386	-808087011072
STPT(10)	916816537918232891	0 2 30 32 60 62 90 92 120 122	-770869775148
SPT(16)	916817085607156033	0 6 24 54 58 94 126 138 196 208 240 276 280 310 328 334	-223180852006
STPT(12)	916817335802999819	0 2 12 14 42 44 168 170 198 200 210 212	27014991780
SPT(16)	916817798157192313	0 30 54 114 154 226 238 244 420 426 438 510 550 610 634 664	489369184274
SPT(16)	916817807523156499	0 22 34 70 72 78 108 114 148 154 184 190 192 228 240 262	498735148460
SPT(18)	916818104085491873	0 24 30 38 96 144 180 194 200 234 240 254 290 338 396 404 410 434	795297483834
TPT(14)	916818154802692949	0 2 30 32 42 44 162 164 198 200 378 380 408 410	846014684910