Prime p₀= 2326715618348583731 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 16 2 22 2 28 2 124 2 70 2 (?)
a_n: 0 2 78 80 96 98 120 122 150 152 276 278 348 350
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: 350
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 76 16 22 28 124 70

SPT(16)	2326714219966967927	0 12 26 42 54 74 84 110 126 152 162 182 194 210 224 236	-1398381615804
STPT(10)	2326714279658358671	0 2 6 8 48 50 90 92 96 98	-1338690225060
SPT(16)	2326714414499455009	0 28 42 78 102 124 138 144 148 154 168 190 214 250 264 292	-1203849128722
TPT(14)	2326714564339013501	0 2 30 32 48 50 78 80 330 332 420 422 438 440	-1054009570230
TPT(14)	2326714903295870159	0 2 42 44 48 50 72 74 78 80 210 212 252 254	-715052713572
SPT(16)	2326715068322413651	0 22 28 36 60 72 82 88 120 126 136 148 172 180 186 208	-550026170080
SPT(16)	2326715659462102897	0 24 30 76 84 114 120 126 184 190 196 226 234 280 286 310	41113519166
SPT(16)	2326715755431862643	0 66 90 144 158 164 168 210 224 266 270 276 290 344 368 434	137083278912
TPT(14)	2326715794493815577	0 2 24 26 84 86 114 116 144 146 150 152 240 242	176145231846
STPT(10)	2326716427976186801	0 2 36 38 78 80 120 122 156 158	809627603070
TPT(16)	2326716683162139467	0 2 24 26 90 92 192 194 234 236 432 434 510 512 552 554	1064813555736