Prime p₀= 2531312496075632909 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 58 2 76 2 40 2 16 2 (?)
a_n: 0 2 78 80 120 122 180 182 258 260 300 302 318 320
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: 320
Found by: [SG-FC] hl
db: batch=82, k=14, 76 40 58 76 40 16

SPT(16)	2531311131664651997	0 84 92 126 152 156 170 192 224 246 260 264 290 324 332 416	-1364410980912
SPT(16)	2531311284408846487	0 30 34 72 132 142 150 172 174 196 204 214 274 312 316 346	-1211666786422
TPT(14)	2531311626555661931	0 2 60 62 198 200 210 212 216 218 258 260 366 368	-869519970978
SPT(16)	2531312047771018823	0 6 36 50 78 98 138 198 236 296 336 356 384 398 428 434	-448304614086
STPT(10)	2531312209471499891	0 2 66 68 108 110 150 152 216 218	-286604133018
SPT(16)	2531312348557467173	0 6 20 24 44 90 96 114 140 158 164 210 230 234 248 254	-147518165736
STPT(10)	2531312762405994989	0 2 78 80 120 122 162 164 240 242	266330362080
SPT(16)	2531313165049385161	0 12 16 18 30 58 60 78 190 208 210 238 250 252 256 268	668973752252
SPT(16)	2531313239381691617	0 6 20 32 62 72 80 90 206 216 224 234 264 276 290 296	743306058708
SPT(16)	2531313299788564091	0 30 36 56 66 80 108 120 128 140 168 182 192 212 218 248	803712931182
STPT(10)	2531313476797720187	0 2 60 62 72 74 84 86 144 146	980722087278