Prime p₀= 778519907496454157 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 34 2 52 2 28 2 4 2 58 2 (?)
a_n: 0 2 24 26 60 62 114 116 144 146 150 152 210 212
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: arkiss
db: batch=73, k=14, 22 34 52 28 4 58

SPT(18)	778519549936749311	0 18 36 78 96 152 176 188 260 318 390 402 426 482 500 542 560 578	-357559704846
SPT(16)	778519558086329903	0 8 48 74 90 126 140 156 158 174 188 224 240 266 306 314	-349410124254
SPT(16)	778519573031259601	0 22 28 36 66 76 106 148 180 222 252 262 292 300 306 328	-334465194556
SPT(16)	778519621006320407	0 2 14 30 86 90 96 152 174 230 236 240 296 312 324 326	-286490133750
SPT(16)	778519702748227789	0 30 84 90 112 154 172 174 220 222 240 282 304 310 364 394	-204748226368
STPT(10)	778519899199312817	0 2 30 32 42 44 54 56 84 86	-8297141340
STPT(10)	778519927965960407	0 2 54 56 132 134 210 212 264 266	20469506250
STPT(10)	778520169371416991	0 2 78 80 138 140 198 200 276 278	261874962834
SPT(16)	778520439613207363	0 34 64 100 108 168 184 190 204 210 226 286 294 330 360 394	532116753206
SPT(16)	778520465632830589	0 22 48 102 160 168 174 210 292 328 334 342 400 454 480 502	558136376432
TPT(14)	778520478403501529	0 2 78 80 132 134 180 182 210 212 222 224 252 254	570907047372