Prime p₀= 2726560597473210761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 34 2 70 2 166 2 22 2 4 2 (?)
a_n: 0 2 90 92 126 128 198 200 366 368 390 392 396 398
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: 398
Found by: Roadranner
db: batch=82, k=14, 88 34 70 166 22 4

SPT(16)	2726559663258453349	0 52 54 84 90 94 130 162 220 252 288 292 298 328 330 382	-934214757412
SPT(16)	2726559675773636933	0 6 74 80 98 114 128 146 318 336 350 366 384 390 458 464	-921699573828
STPT(10)	2726559773636866589	0 2 78 80 120 122 162 164 240 242	-823836344172
STPT(10)	2726560025866385237	0 2 60 62 72 74 84 86 144 146	-571606825524
TPT(14)	2726560418194103759	0 2 78 80 90 92 132 134 162 164 210 212 228 230	-179279107002
SPT(16)	2726560506819672101	0 8 20 62 98 120 138 152 216 230 248 270 306 348 360 368	-90653538660
SPT(16)	2726560613407385437	0 4 40 60 106 112 130 132 154 156 174 180 226 246 282 286	15934174676
STPT(10)	2726560757460584459	0 2 18 20 30 32 42 44 60 62	159987373698
STPT(10)	2726561044074518237	0 2 30 32 72 74 114 116 144 146	446601307476
SPT(16)	2726561142914953301	0 26 38 42 146 170 200 248 300 348 378 402 506 510 522 548	545441742540
STPT(10)	2726561821289826731	0 2 30 32 78 80 126 128 156 158	1223816615970