Prime p₀= 2892429501355496759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 178 2 46 2 22 2 58 2 34 2 40 2 (?)
a_n: 0 2 180 182 228 230 252 254 312 314 348 350 390 392
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: 392
Found by: JonS
db: batch=82, k=14, 178 46 22 58 34 40

SPT(16)	2892428234310669337	0 12 30 54 70 100 114 132 142 160 174 204 220 244 262 274	-1267044827422
SPT(16)	2892428701653880693	0 16 30 40 78 90 108 124 150 166 184 196 234 244 258 274	-799701616066
TPT(14)	2892428736395621999	0 2 78 80 162 164 168 170 198 200 210 212 270 272	-764959874760
STPT(12)	2892428819075037029	0 2 30 32 72 74 168 170 210 212 240 242	-682280459730
SPT(16)	2892428943273401743	0 28 58 66 70 78 106 150 154 198 226 234 238 246 276 304	-558082095016
STPT(10)	2892429210113074127	0 2 60 62 72 74 84 86 144 146	-291242422632
TPT(14)	2892429646506163217	0 2 24 26 42 44 84 86 102 104 210 212 240 242	145150666458
SPT(16)	2892430020463190491	0 70 78 88 118 130 142 168 202 228 240 252 282 292 300 370	519107693732
STPT(10)	2892430105622032271	0 2 6 8 18 20 30 32 36 38	604266535512
SPT(16)	2892430143740854273	0 40 90 118 120 148 238 270 274 306 396 424 426 454 504 544	642385357514
STPT(10)	2892430147037219021	0 2 30 32 78 80 126 128 156 158	645681722262