Prime p₀= 2867406764090321657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 10 2 64 2 28 2 22 2 16 2 (?)
a_n: 0 2 72 74 84 86 150 152 180 182 204 206 222 224
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: 224
Found by: JohnMD
db: batch=82, k=14, 70 10 64 28 22 16

TPT(14)	2867404902353991341	0 2 108 110 198 200 270 272 276 278 396 398 408 410	-1861736330316
STPT(10)	2867405411099510891	0 2 30 32 78 80 126 128 156 158	-1352990810766
STPT(10)	2867405791995605087	0 2 54 56 132 134 210 212 264 266	-972094716570
SPT(18)	2867406097899824837	0 6 14 66 110 114 132 170 180 266 276 314 332 336 380 432 440 446	-666190496820
STPT(10)	2867406563989863947	0 2 42 44 102 104 162 164 204 206	-200100457710
SPT(20)	2867406717090536119	0 10 22 24 30 52 90 108 118 148 204 234 244 262 300 322 328 330 342 352	-46999785538
SPT(16)	2867406984142796939	0 98 120 128 140 158 180 194 228 242 264 282 294 302 324 422	220052475282
SPT(16)	2867407185735332561	0 12 110 128 140 230 242 252 338 348 360 450 462 480 578 590	421645010904
SPT(16)	2867407599156320443	0 6 10 46 48 66 94 100 144 150 178 196 198 234 238 244	835065998786
SPT(13)	2867407801062802951	0 42 72 162 198 210 240 270 282 318 408 438 480	1036972481294
SPT(16)	2867407841168015989	0 22 142 160 162 244 250 264 268 282 288 370 372 390 510 532	1077077694332