Prime p₀= 2768626734506794541 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 178 2 100 2 40 2 148 2 58 2 (?)
a_n: 0 2 6 8 186 188 288 290 330 332 480 482 540 542
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: 542
Found by: RFGuy_KCCO
db: batch=82, k=14, 4 178 100 40 148 58

SPT(18)	2768624889901628939	0 48 54 60 102 108 132 140 158 174 192 200 224 230 272 278 284 332	-1844605165602
STPT(10)	2768625092753468747	0 2 30 32 120 122 210 212 240 242	-1641753325794
SPT(16)	2768625478707885211	0 16 60 70 72 78 100 106 192 198 220 226 228 238 282 298	-1255798909330
TPT(14)	2768625676260176261	0 2 18 20 60 62 90 92 126 128 156 158 216 218	-1058246618280
STPT(10)	2768626139057626877	0 2 12 14 42 44 72 74 84 86	-595449167664
SPT(16)	2768626183847805511	0 42 46 48 60 66 76 126 142 192 202 208 220 222 226 268	-550658989030
STPT(10)	2768626806689662727	0 2 54 56 72 74 90 92 144 146	72182868186
SPT(16)	2768627143478055611	0 38 66 96 140 168 258 290 306 338 428 456 500 530 558 596	408971261070
SPT(18)	2768627278587019793	0 14 38 66 80 84 86 146 150 164 168 228 230 234 248 276 300 314	544080225252
SPT(16)	2768627409957008359	0 42 70 84 112 114 148 162 250 264 298 300 328 342 370 412	675450213818
SPT(16)	2768627549935928081	0 8 38 60 92 168 170 176 192 198 200 276 308 330 360 368	815429133540