Prime p₀= 2166868354830865667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 46 2 10 2 10 2 4 2 22 2 (?)
a_n: 0 2 42 44 90 92 102 104 114 116 120 122 144 146
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: 146
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 40 46 10 10 4 22

TPT(14)	2166867608576411591	0 2 30 32 48 50 168 170 210 212 240 242 270 272	-746254454076
STPT(10)	2166867958119542537	0 2 30 32 72 74 114 116 144 146	-396711323130
SPT(16)	2166868001752633843	0 10 30 46 60 70 76 88 96 108 114 124 138 154 174 184	-353078231824
STPT(10)	2166868009133282639	0 2 30 32 60 62 90 92 120 122	-345697583028
SPT(16)	2166868170534461621	0 12 36 42 110 188 192 206 222 236 240 318 386 392 416 428	-184296404046
STPT(10)	2166868307052644147	0 2 30 32 42 44 54 56 84 86	-47778221520
SPT(16)	2166868390703908223	0 134 204 224 236 246 248 288 296 336 338 348 360 380 450 584	35873042556
STPT(10)	2166868422096629567	0 2 30 32 42 44 54 56 84 86	67265763900
SPT(16)	2166868424778096007	0 12 22 36 52 70 114 156 160 202 246 264 280 294 304 316	69947230340
STPT(10)	2166868665921534389	0 2 12 14 90 92 168 170 180 182	311090668722
STPT(10)	2166868675845313211	0 2 36 38 78 80 120 122 156 158	321014447544