Prime p₀= 2796998981323632101 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 94 2 70 2 136 2 10 2 (?)
a_n: 0 2 30 32 90 92 186 188 258 260 396 398 408 410
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: 410
Found by: JohnMD
db: batch=82, k=14, 28 58 94 70 136 10

SPT(16)	2796997633650262247	0 24 30 44 50 62 90 102 104 116 144 156 162 176 182 206	-1347673369854
SPT(16)	2796997815952452647	0 44 66 146 150 152 212 216 230 234 294 296 300 380 402 446	-1165371179454
SPT(16)	2796997816696231229	0 8 68 72 78 152 188 212 228 252 288 362 368 372 432 440	-1164627400872
SPT(16)	2796997830826950713	0 6 14 30 50 84 96 156 158 218 230 264 284 300 308 314	-1150496681388
STPT(10)	2796997924944622541	0 2 6 8 18 20 30 32 36 38	-1056379009560
STPT(10)	2796998715113703167	0 2 12 14 42 44 72 74 84 86	-266209928934
STPT(10)	2796999422286639539	0 2 12 14 30 32 48 50 60 62	440963007438
SPT(16)	2796999742551642379	0 48 72 118 148 178 198 252 268 322 342 372 402 448 472 520	761228010278
SPT(16)	2796999965920837603	0 54 120 160 238 268 300 328 330 358 390 420 498 538 604 658	984597205502
TPT(14)	2796999989114596127	0 2 30 32 42 44 90 92 102 104 144 146 174 176	1007790964026
TPT(14)	2797000013802093401	0 2 30 32 78 80 96 98 108 110 210 212 306 308	1032478461300