Prime p₀= 2956912803665993057 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 88 2 10 2 28 2 34 2 58 2 (?)
a_n: 0 2 42 44 132 134 144 146 174 176 210 212 270 272
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, 40 88 10 28 34 58

SPT(16)	2956911141201520301	0 30 50 66 80 102 126 156 212 242 266 288 302 318 338 368	-1662464472756
STPT(12)	2956911848494657169	0 2 30 32 72 74 138 140 180 182 210 212	-955171335888
SPT(16)	2956911964364835193	0 40 54 90 106 120 124 160 210 246 250 264 280 316 330 370	-839301157864
TPT(14)	2956912138595156321	0 2 66 68 108 110 138 140 156 158 180 182 270 272	-665070836736
SPT(18)	2956912367841620509	0 18 24 28 54 72 88 112 142 180 210 234 250 268 294 298 304 322	-435824372548
SPT(16)	2956912735389148169	0 12 14 30 32 72 128 132 140 144 200 240 242 258 260 272	-68276844888
STPT(10)	2956912929665242517	0 2 54 56 72 74 90 92 144 146	125999249460
SPT(16)	2956913253882393101	0 18 36 50 92 116 140 150 158 168 192 216 258 272 290 308	450216400044
SPT(16)	2956913309221243667	0 36 54 92 162 176 180 192 224 236 240 254 324 362 380 416	505555250610
SPT(16)	2956913490718203971	0 26 48 96 182 198 216 236 282 302 320 336 422 470 492 518	687052210914
TPT(14)	2956913533835632079	0 2 18 20 60 62 102 104 198 200 300 302 372 374	730169639022