Prime p₀= 2316582969011629361 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 40 2 16 2 172 2 16 2 28 2 (?)
a_n: 0 2 96 98 138 140 156 158 330 332 348 350 378 380
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: 380
Found by: Orange Kid
db: batch=81, k=14, 94 40 16 172 16 28

SPT(16)	2316582433619549911	0 6 18 40 46 76 88 112 186 210 222 252 258 280 292 298	-535392079450
SPT(16)	2316582543866427751	0 10 18 40 52 66 70 136 162 228 232 246 258 280 288 298	-425145201610
STPT(10)	2316582769612705331	0 2 78 80 108 110 138 140 216 218	-199398924030
SPT(16)	2316582805451045513	0 18 26 54 74 104 120 126 188 194 210 240 260 288 296 314	-163560583848
STPT(10)	2316582842998002791	0 2 36 38 78 80 120 122 156 158	-126013626570
SPT(16)	2316582867888407809	0 22 48 70 84 94 132 150 172 190 228 238 252 274 300 322	-101123221552
SPT(16)	2316583095411263179	0 34 64 70 72 78 88 100 102 114 124 130 132 138 168 202	126399633818
STPT(10)	2316584601579156287	0 2 30 32 42 44 54 56 84 86	1632567526926
SPT(16)	2316585049587489269	0 18 44 50 54 84 114 120 218 224 254 284 288 294 320 338	2080575859908
SPT(16)	2316585362412958009	0 114 130 150 172 174 192 214 240 262 280 282 304 324 340 454	2393401328648
TPT(14)	2316585428577171539	0 2 12 14 72 74 138 140 168 170 210 212 300 302	2459565542178