Prime p₀= 2812580068748733431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 10 2 40 2 46 2 10 2 64 2 (?)
a_n: 0 2 96 98 108 110 150 152 198 200 210 212 276 278
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: 278
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 94 10 40 46 10 64

SPT(22)	2812579085744590493	0 14 30 36 50 56 74 140 144 146 170 174 198 200 204 270 288 294 308 314 330 344	-983004142938
SPT(16)	2812579115880931333	0 4 6 24 34 58 70 88 96 114 126 150 160 178 180 184	-952867802098
SPT(16)	2812579210674854741	0 30 32 92 96 120 126 128 150 152 158 182 186 246 248 278	-858073878690
SPT(16)	2812579265058842407	0 30 76 90 112 120 156 160 186 190 226 234 256 270 316 346	-803689891024
STPT(10)	2812579680643221017	0 2 60 62 72 74 84 86 144 146	-388105512414
SPT(18)	2812579728382537661	0 8 18 38 56 62 78 80 116 132 168 170 186 192 210 230 240 248	-340366195770
SPT(16)	2812580069389152473	0 24 66 80 90 110 140 144 230 234 264 284 294 308 350 374	640419042
TPT(14)	2812580275920223811	0 2 6 8 36 38 60 62 90 92 156 158 210 212	207171490380
STPT(10)	2812580539261008287	0 2 72 74 102 104 132 134 204 206	470512274856
SPT(16)	2812580589318404783	0 50 60 84 116 128 170 204 260 294 336 348 380 404 414 464	520569671352
STPT(10)	2812580835876388301	0 2 6 8 48 50 90 92 96 98	767127654870