Prime p₀= 2797020338554427471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 40 2 124 2 10 2 40 2 (?)
a_n: 0 2 66 68 78 80 120 122 246 248 258 260 300 302
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: 302
Found by: Time_Traveler
db: batch=82, k=14, 64 10 40 124 10 40

SPT(16)	2797019116325862161	0 2 38 110 138 156 158 200 318 360 362 380 408 480 516 518	-1222228565310
SPT(16)	2797019347826305559	0 20 60 90 132 150 152 174 200 222 224 242 284 314 354 374	-990728121912
SPT(16)	2797019872220639833	0 4 10 18 34 36 60 76 78 94 118 120 136 144 150 154	-466333787638
STPT(10)	2797019920657863947	0 2 12 14 72 74 132 134 144 146	-417896563524
TPT(14)	2797020070623426077	0 2 84 86 150 152 180 182 222 224 264 266 300 302	-267931001394
SPT(16)	2797020336282510587	0 2 12 14 30 36 42 60 86 104 110 116 132 134 144 146	-2271916884
SPT(16)	2797020455892629731	0 6 42 46 88 120 160 162 196 198 238 270 312 316 352 358	117338202260
TPT(14)	2797020597626817389	0 2 18 20 42 44 48 50 78 80 168 170 198 200	259072389918
SPT(16)	2797020868377332227	0 16 30 42 46 70 96 186 220 310 336 360 364 376 390 406	529822904756
SPT(16)	2797021277705069197	0 6 12 70 90 94 126 180 256 310 342 346 366 424 430 436	939150641726
TPT(14)	2797021360173495821	0 2 36 38 90 92 156 158 168 170 246 248 288 290	1021619068350