Prime p₀= 2709067792550968727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 22 2 16 2 10 2 16 2 (?)
a_n: 0 2 30 32 60 62 84 86 102 104 114 116 132 134
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: 134
Found by: JohnMD
db: batch=82, k=14, 28 28 22 16 10 16

SPT(16)	2709067036565005073	0 14 26 44 84 86 110 116 138 144 168 170 210 228 240 254	-755985963654
STPT(10)	2709067361130835631	0 2 36 38 108 110 180 182 216 218	-431420133096
STPT(10)	2709067388589930461	0 2 30 32 60 62 90 92 120 122	-403961038266
SPT(16)	2709067495091443193	0 26 38 54 68 80 140 158 246 264 324 336 350 366 378 404	-297459525534
SPT(16)	2709067749123863161	0 6 12 30 40 66 108 112 156 160 202 228 238 256 262 268	-43427105566
SPT(16)	2709067791261869237	0 12 44 56 102 114 126 146 180 200 212 224 270 282 314 326	-1289099490
STPT(10)	2709068338917073919	0 2 42 44 60 62 78 80 120 122	546366105192
TPT(14)	2709068969986131407	0 2 54 56 114 116 144 146 174 176 180 182 210 212	1177435162680
STPT(12)	2709069106017233747	0 2 12 14 30 32 54 56 72 74 84 86	1313466265020
SPT(13)	2709069694571298781	0 42 66 72 120 150 156 162 192 240 246 270 312	1902020330054
SPT(16)	2709069764634337319	0 80 90 98 108 140 210 234 248 272 342 374 384 392 402 482	1972083368592