Prime p₀= 2340578631220915199 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 40 2 28 2 46 2 58 2 (?)
a_n: 0 2 30 32 90 92 132 134 162 164 210 212 270 272
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: 272
Found by: Landjunge
db: batch=81, k=14, 28 58 40 28 46 58

TPT(14)	2340576294487188887	0 2 42 44 84 86 120 122 180 182 192 194 204 206	-2336733726312
SPT(16)	2340576348787213331	0 6 32 56 72 90 92 120 182 210 212 230 246 270 296 302	-2282433701868
STPT(10)	2340577161128423489	0 2 18 20 30 32 42 44 60 62	-1470092491710
STPT(10)	2340577358892183767	0 2 42 44 72 74 102 104 144 146	-1272328731432
SPT(16)	2340577623669878399	0 14 42 48 104 108 144 162 170 188 224 228 284 290 318 332	-1007551036800
TPT(14)	2340577746782389181	0 2 6 8 138 140 156 158 168 170 198 200 240 242	-884438526018
STPT(10)	2340579292369447247	0 2 24 26 42 44 60 62 84 86	661148532048
STPT(10)	2340579774189561647	0 2 30 32 42 44 54 56 84 86	1142968646448
SPT(16)	2340579929892246701	0 18 26 72 102 110 156 306 422 572 618 626 656 702 710 728	1298671331502
SPT(16)	2340579999251562053	0 14 96 108 128 140 164 188 216 240 264 276 296 308 390 404	1368030646854
SPT(16)	2340580926045265909	0 42 64 88 90 130 148 150 172 174 192 232 234 258 280 322	2294824350710