Prime p₀= 2726559301255069199 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 58 2 16 2 316 2 40 2 28 2 (?)
a_n: 0 2 132 134 192 194 210 212 528 530 570 572 600 602
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: 602
Found by: Roadranner
db: batch=82, k=14, 130 58 16 316 40 28

TPT(14)	2726558156237224667	0 2 24 26 42 44 150 152 180 182 222 224 252 254	-1145017844532
STPT(12)	2726558590950922529	0 2 72 74 102 104 138 140 168 170 240 242	-710304146670
SPT(16)	2726558788140041689	0 28 48 64 70 84 118 174 184 240 274 288 294 310 330 358	-513115027510
STPT(10)	2726559057166823909	0 2 30 32 60 62 90 92 120 122	-244088245290
SPT(16)	2726559188807668189	0 148 150 210 222 240 282 292 348 358 400 418 430 490 492 640	-112447401010
SPT(16)	2726559250560010387	0 12 30 36 70 90 130 142 144 156 196 216 250 256 274 286	-50695058812
STPT(10)	2726559415033698857	0 2 30 32 42 44 54 56 84 86	113778629658
SPT(16)	2726559663258453349	0 52 54 84 90 94 130 162 220 252 288 292 298 328 330 382	362003384150
SPT(16)	2726559675773636933	0 6 74 80 98 114 128 146 318 336 350 366 384 390 458 464	374518567734
STPT(10)	2726559773636866589	0 2 78 80 120 122 162 164 240 242	472381797390
STPT(10)	2726560025866385237	0 2 60 62 72 74 84 86 144 146	724611316038