Prime p₀= 1009004203588747901 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 40 2 16 2 10 2 58 2 (?)
a_n: 0 2 36 38 78 80 120 122 138 140 150 152 210 212
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: 212
Found by: HenkM
db: batch=76, k=14, 34 40 40 16 10 58

SPT(16)	1009001836642915351	0 10 42 70 78 108 112 126 172 186 190 220 228 256 288 298	-2366945832550
SPT(16)	1009002088852989391	0 46 58 72 102 112 118 130 168 180 186 196 226 240 252 298	-2114735758510
STPT(10)	1009002337916416601	0 2 6 8 18 20 30 32 36 38	-1865672331300
TPT(14)	1009003009128541289	0 2 18 20 78 80 90 92 132 134 168 170 252 254	-1194460206612
STPT(10)	1009003539966488201	0 2 36 38 78 80 120 122 156 158	-663622259700
TPT(14)	1009003735795792859	0 2 48 50 180 182 288 290 330 332 348 350 378 380	-467792955042
SPT(16)	1009004286424392677	0 56 66 72 74 90 144 156 200 212 266 282 284 290 300 356	82835644776
STPT(10)	1009004372701816187	0 2 12 14 72 74 132 134 144 146	169113068286
SPT(16)	1009004812058999597	0 20 50 72 132 134 144 200 216 272 282 284 344 366 396 416	608470251696
SPT(16)	1009004911455261569	0 92 98 104 120 168 188 210 212 234 254 302 318 324 330 422	707866513668
SPT(16)	1009005118259039197	0 22 46 64 66 84 130 142 204 216 262 280 282 300 324 346	914670291296