Prime p₀= 2531821756196150387 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 28 2 52 2 34 2 88 2 (?)
a_n: 0 2 30 32 60 62 90 92 144 146 180 182 270 272
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: Roadranner
db: batch=82, k=14, 28 28 28 52 34 88

SPT(16)	2531820108104091367	0 10 16 30 52 66 162 190 246 274 370 384 406 420 426 436	-1648092059020
STPT(10)	2531820143699224457	0 2 72 74 102 104 132 134 204 206	-1612496925930
STPT(10)	2531820157565298491	0 2 78 80 108 110 138 140 216 218	-1598630851896
STPT(10)	2531820496307739821	0 2 30 32 60 62 90 92 120 122	-1259888410566
TPT(14)	2531820822884293319	0 2 78 80 162 164 240 242 390 392 408 410 450 452	-933311857068
SPT(16)	2531821605761202977	0 14 50 54 56 120 150 216 224 290 320 384 386 390 426 440	-150434947410
SPT(16)	2531821876840652549	0 14 20 60 90 102 104 140 192 228 230 242 272 312 318 332	120644502162
SPT(16)	2531822125735782379	0 22 34 58 100 112 114 174 178 238 240 252 294 318 330 352	369539631992
SPT(16)	2531822273404431487	0 6 22 30 76 102 106 142 174 210 214 240 286 294 310 316	517208281100
SPT(16)	2531822322174457759	0 10 12 18 24 42 52 54 88 90 100 118 124 130 132 142	565978307372
STPT(10)	2531822588333061641	0 2 36 38 78 80 120 122 156 158	832136911254