Prime p₀= 2868923676548409869 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 28 2 4 2 58 2 10 2 58 2 (?)
a_n: 0 2 102 104 132 134 138 140 198 200 210 212 270 272
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: 272
Found by: [SG-FC] hl
db: batch=82, k=14, 100 28 4 58 10 58

SPT(16)	2868922694114591251	0 16 22 48 82 90 132 156 172 196 238 246 280 306 312 328	-982433818618
STPT(10)	2868922808364387959	0 2 30 32 60 62 90 92 120 122	-868184021910
SPT(16)	2868922846735135657	0 24 42 70 76 84 120 126 130 136 172 180 186 214 232 256	-829813274212
TPT(14)	2868922873560655211	0 2 60 62 126 128 150 152 156 158 198 200 240 242	-802987754658
STPT(10)	2868923139095129759	0 2 102 104 210 212 318 320 420 422	-537453280110
STPT(10)	2868923284624634009	0 2 12 14 90 92 168 170 180 182	-391923775860
STPT(10)	2868923973199390199	0 2 42 44 60 62 78 80 120 122	296650980330
SPT(16)	2868924017973316613	0 30 50 84 116 120 140 156 254 270 290 294 326 360 380 410	341424906744
TPT(14)	2868924052071466601	0 2 36 38 78 80 90 92 156 158 168 170 186 188	375523056732
STPT(10)	2868924643085496011	0 2 30 32 78 80 126 128 156 158	966537086142
SPT(16)	2868924749548854089	0 14 18 42 74 144 164 210 242 288 308 378 410 434 438 452	1073000444220