Prime p₀= 2078720628923226851 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 28 2 112 2 64 2 22 2 16 2 (?)
a_n: 0 2 66 68 96 98 210 212 276 278 300 302 318 320
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: 320
Found by: vaughan
db: batch=80, k=14, 64 28 112 64 22 16

SPT(16)	2078719255539508781	0 2 6 20 36 42 50 90 122 162 170 176 192 206 210 212	-1373383718070
TPT(14)	2078719266766679399	0 2 18 20 78 80 102 104 210 212 252 254 330 332	-1362156547452
SPT(16)	2078719303585714453	0 10 30 94 100 108 114 144 250 280 286 294 300 364 384 394	-1325337512398
SPT(16)	2078719847873974469	0 54 72 92 132 164 194 230 324 360 390 422 462 482 500 554	-781049252382
SPT(16)	2078720126619981001	0 42 48 106 126 148 216 238 240 262 330 352 372 430 436 478	-502303245850
STPT(10)	2078720208653988869	0 2 12 14 30 32 48 50 60 62	-420269237982
SPT(16)	2078720835887584153	0 30 94 124 154 168 180 184 210 214 226 240 270 300 364 394	206964357302
STPT(10)	2078720891587594757	0 2 24 26 42 44 60 62 84 86	262664367906
SPT(16)	2078721102921072437	0 32 66 84 90 102 182 200 216 234 314 326 332 350 384 416	473997845586
STPT(10)	2078721137978019707	0 2 12 14 72 74 132 134 144 146	509054792856
SPT(16)	2078721166539064753	0 30 46 60 66 84 90 94 216 220 226 244 250 264 280 310	537615837902