Prime p₀= 2811528891139188767 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 172 2 16 2 16 2 10 2 10 2 (?)
a_n: 0 2 30 32 204 206 222 224 240 242 252 254 264 266
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: 266
Found by: JayPi
db: batch=82, k=14, 28 172 16 16 10 10

SPT(16)	2811527848745975581	0 6 28 66 88 112 160 180 208 228 276 300 322 360 382 388	-1042393213186
SPT(13)	2811527871413193169	0 18 90 108 168 228 234 240 300 360 378 450 468	-1019725995598
SPT(16)	2811528070304651567	0 6 20 42 56 60 62 72 74 84 86 90 104 126 140 146	-820834537200
SPT(16)	2811528242968074907	0 60 106 120 160 162 172 202 300 330 340 342 382 396 442 502	-648171113860
TPT(14)	2811528287290303277	0 2 12 14 54 56 72 74 102 104 114 116 132 134	-603848885490
SPT(16)	2811528452392052317	0 40 52 60 70 82 96 144 172 220 234 246 256 264 276 316	-438747136450
SPT(16)	2811529315764782101	0 10 16 42 46 58 88 112 126 150 180 192 196 222 228 238	424625593334
TPT(14)	2811529317145914509	0 2 72 74 102 104 282 284 300 302 390 392 408 410	426006725742
SPT(16)	2811529687436195749	0 18 28 48 64 90 162 214 228 280 352 378 394 414 424 442	796297006982
STPT(10)	2811529871932230341	0 2 6 8 48 50 90 92 96 98	980793041574
SPT(16)	2811529932783049817	0 14 42 50 62 72 80 84 170 174 182 192 204 212 240 254	1041643861050