Prime p₀= 2109841781147178917 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 88 2 34 2 100 2 58 2 10 2 (?)
a_n: 0 2 24 26 114 116 150 152 252 254 312 314 324 326
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: 326
Found by: Landjunge
db: batch=80, k=14, 22 88 34 100 58 10

SPT(16)	2109839417660969251	0 6 28 52 88 112 132 138 160 166 186 210 246 270 292 298	-2363486209666
SPT(16)	2109839684433672391	0 12 70 72 82 90 162 166 282 286 358 366 376 378 436 448	-2096713506526
STPT(10)	2109839838750798569	0 2 18 20 30 32 42 44 60 62	-1942396380348
SPT(16)	2109839847583968679	0 48 78 82 124 138 144 202 210 268 274 288 330 334 364 412	-1933563210238
SPT(16)	2109840212056436999	0 24 62 80 104 110 138 144 188 194 222 228 252 270 308 332	-1569090741918
SPT(16)	2109840853206091441	0 16 46 90 112 126 178 190 198 210 262 276 298 342 372 388	-927941087476
SPT(16)	2109841806916568723	0 48 174 194 224 228 264 284 300 320 356 360 390 410 536 584	25769389806
STPT(10)	2109842073555023837	0 2 30 32 42 44 54 56 84 86	292407844920
STPT(10)	2109842093468906507	0 2 12 14 42 44 72 74 84 86	312321727590
STPT(10)	2109842263571591567	0 2 42 44 72 74 102 104 144 146	482424412650
STPT(10)	2109842291007620591	0 2 36 38 78 80 120 122 156 158	509860441674