Prime p₀= 2773936215117862757 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 112 2 28 2 4 2 40 2 58 2 (?)
a_n: 0 2 30 32 144 146 174 176 180 182 222 224 282 284
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: 284
Found by: JayPi
db: batch=82, k=14, 28 112 28 4 40 58

SPT(16)	2773934163682187041	0 12 28 40 42 48 112 120 130 138 202 208 210 222 238 250	-2051435675716
STPT(10)	2773934338670567921	0 2 30 32 60 62 90 92 120 122	-1876447294836
STPT(10)	2773935504796194587	0 2 30 32 60 62 90 92 120 122	-710321668170
SPT(16)	2773935598950940517	0 30 60 74 90 122 144 164 192 212 234 266 282 296 326 356	-616166922240
SPT(16)	2773936130421069007	0 4 34 64 84 94 120 150 154 184 210 220 240 270 300 304	-84696793750
TPT(14)	2773936172171471579	0 2 18 20 72 74 138 140 192 194 198 200 312 314	-42946391178
STPT(10)	2773936515073251887	0 2 60 62 102 104 144 146 204 206	299955389130
SPT(16)	2773937029988164127	0 24 90 96 152 174 234 246 350 362 422 444 500 506 572 596	814870301370
SPT(16)	2773937046258457007	0 26 42 56 66 90 122 152 264 294 326 350 360 374 390 416	831140594250
SPT(16)	2773937120993760091	0 30 52 76 118 156 166 198 220 252 262 300 342 366 388 418	905875897334
SPT(16)	2773937158949381329	0 58 84 90 114 168 192 202 210 220 244 298 322 328 354 412	943831518572