Prime p₀= 2864951794352180471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 58 2 28 2 106 2 40 2 (?)
a_n: 0 2 78 80 120 122 180 182 210 212 318 320 360 362
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: 362
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 76 40 58 28 106 40

STPT(10)	2864949971273570261	0 2 6 8 48 50 90 92 96 98	-1823078610210
STPT(10)	2864950358711023379	0 2 18 20 30 32 42 44 60 62	-1435641157092
SPT(16)	2864950694943200609	0 18 20 62 102 144 188 198 254 264 308 350 390 432 434 452	-1099408979862
SPT(16)	2864950830148316603	0 26 36 126 128 144 150 168 236 254 260 276 278 368 378 404	-964203863868
STPT(10)	2864951092800874697	0 2 42 44 72 74 102 104 144 146	-701551305774
STPT(10)	2864951757912578681	0 2 6 8 48 50 90 92 96 98	-36439601790
SPT(16)	2864952094116545327	0 42 114 144 152 164 170 200 264 294 300 312 320 350 422 464	299764364856
SPT(16)	2864952336754182877	0 12 16 30 42 70 72 96 100 124 126 154 166 180 184 196	542402002406
SPT(18)	2864952888789185021	0 2 6 18 38 48 50 80 98 150 168 198 200 210 230 242 246 248	1094437004550
SPT(16)	2864952915888928421	0 6 18 50 90 96 102 116 162 176 182 188 228 260 272 278	1121536747950
SPT(16)	2864953465337520103	0 18 54 60 66 94 148 156 178 186 240 268 274 280 316 334	1670985339632