Prime p₀= 2956912138595156321 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 28 2 16 2 22 2 88 2 (?)
a_n: 0 2 66 68 108 110 138 140 156 158 180 182 270 272
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: 272
Found by: Orange Kid
db: batch=82, k=14, 64 40 28 16 22 88

STPT(10)	2956910345287656809	0 2 18 20 60 62 102 104 120 122	-1793307499512
STPT(10)	2956910434618296941	0 2 36 38 78 80 120 122 156 158	-1703976859380
SPT(16)	2956911088542602053	0 4 10 36 64 76 84 88 276 280 288 300 328 354 360 364	-1050052554268
SPT(16)	2956911141201520301	0 30 50 66 80 102 126 156 212 242 266 288 302 318 338 368	-997393636020
STPT(12)	2956911848494657169	0 2 30 32 72 74 138 140 180 182 210 212	-290100499152
SPT(16)	2956911964364835193	0 40 54 90 106 120 124 160 210 246 250 264 280 316 330 370	-174230321128
SPT(18)	2956912367841620509	0 18 24 28 54 72 88 112 142 180 210 234 250 268 294 298 304 322	229246464188
SPT(16)	2956912735389148169	0 12 14 30 32 72 128 132 140 144 200 240 242 258 260 272	596793991848
TPT(14)	2956912803665993057	0 2 42 44 132 134 144 146 174 176 210 212 270 272	665070836736
STPT(10)	2956912929665242517	0 2 54 56 72 74 90 92 144 146	791070086196
SPT(16)	2956913253882393101	0 18 36 50 92 116 140 150 158 168 192 216 258 272 290 308	1115287236780