Prime p₀= 2688107949916922711 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 58 2 10 2 10 2 4 2 22 2 (?)
a_n: 0 2 6 8 66 68 78 80 90 92 96 98 120 122
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: 122
Found by: biodoc
db: batch=82, k=14, 4 58 10 10 4 22

SPT(16)	2688107068000473773	0 20 24 38 90 134 180 206 318 344 390 434 486 500 504 524	-881916448938
SPT(16)	2688107155962555193	0 28 40 48 58 88 100 124 144 168 180 210 220 228 240 268	-793954367518
SPT(16)	2688107391607565243	0 30 66 114 128 156 194 198 206 210 248 276 290 338 374 404	-558309357468
TPT(14)	2688107524299909587	0 2 12 14 30 32 54 56 72 74 120 122 192 194	-425617013124
SPT(16)	2688107787857228623	0 6 40 54 108 178 220 238 276 294 336 406 460 474 508 514	-162059694088
STPT(10)	2688107828650716959	0 2 48 50 90 92 132 134 180 182	-121266205752
STPT(10)	2688108055082426687	0 2 42 44 72 74 102 104 144 146	105165503976
SPT(16)	2688108083153890897	0 22 34 82 120 126 136 142 174 180 190 196 234 282 294 316	133236968186
STPT(10)	2688108429141356069	0 2 30 32 60 62 90 92 120 122	479224433358
STPT(10)	2688108444564002147	0 2 30 32 120 122 210 212 240 242	494647079436
STPT(10)	2688108532777016717	0 2 30 32 42 44 54 56 84 86	582860094006