Prime p₀= 2780581360941281759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 136 2 22 2 34 2 22 2 16 2 10 2 (?)
a_n: 0 2 138 140 162 164 198 200 222 224 240 242 252 254
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: 254
Found by: JayPi
db: batch=82, k=14, 136 22 34 22 16 10

TPT(14)	2780578807075792397	0 2 24 26 162 164 174 176 204 206 360 362 462 464	-2553865489362
SPT(16)	2780579682944623957	0 52 60 102 112 144 154 172 174 192 202 234 244 286 294 346	-1677996657802
STPT(10)	2780580090366373751	0 2 30 32 78 80 126 128 156 158	-1270574908008
SPT(16)	2780580879815834357	0 42 84 86 104 114 120 132 164 176 182 192 210 212 254 296	-481125447402
SPT(16)	2780581141115845997	0 24 44 80 86 102 114 140 156 182 194 210 216 252 272 296	-219825435762
STPT(10)	2780581260904596197	0 2 42 44 72 74 102 104 144 146	-100036685562
TPT(16)	2780581425971560361	0 2 36 38 96 98 150 152 276 278 306 308 426 428 558 560	65030278602
STPT(10)	2780582269189553891	0 2 18 20 168 170 318 320 336 338	908248272132
SPT(16)	2780582422750883419	0 4 40 114 138 184 204 238 240 274 294 340 364 438 474 478	1061809601660
STPT(10)	2780582508204552809	0 2 18 20 30 32 42 44 60 62	1147263271050
SPT(16)	2780582642433536321	0 2 6 30 56 68 72 86 192 206 210 222 248 272 276 278	1281492254562