Prime p₀= 910344158457830387 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 28 2 76 2 10 2 40 2 (?)
a_n: 0 2 30 32 102 104 132 134 210 212 222 224 264 266
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: 266
Found by: [SG]FX
db: batch=76, k=14, 28 70 28 76 10 40

SPT(16)	910342734053350379	0 38 42 48 74 80 92 108 134 150 162 168 194 200 204 242	-1424404480008
STPT(10)	910342758517610027	0 2 30 32 42 44 54 56 84 86	-1399940220360
STPT(10)	910342772197360259	0 2 18 20 30 32 42 44 60 62	-1386260470128
STPT(10)	910342827008831297	0 2 54 56 72 74 90 92 144 146	-1331448999090
SPT(16)	910342880669354333	0 6 18 36 56 66 80 108 158 186 200 210 230 248 260 266	-1277788476054
SPT(16)	910343383016013761	0 8 20 36 42 48 66 92 96 122 140 146 152 168 180 188	-775441816626
SPT(16)	910344226732931521	0 6 12 18 58 156 168 222 256 310 322 420 460 466 472 478	68275101134
SPT(20)	910344255390918923	0 24 44 84 98 134 164 176 198 276 308 386 408 420 450 486 500 540 560 584	96933088536
STPT(10)	910344579174537977	0 2 30 32 42 44 54 56 84 86	420716707590
SPT(16)	910344624767997253	0 4 18 118 148 154 168 238 246 316 330 336 366 466 480 484	466310166866
SPT(18)	910344944166016453	0 34 40 48 58 64 76 94 100 174 180 198 210 216 226 234 240 274	785708186066