Prime p₀= 1268810840309167709 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 106 2 58 2 46 2 88 2 22 2 (?)
a_n: 0 2 72 74 180 182 240 242 288 290 378 380 402 404
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: 404
Found by: Megacruncher
db: batch=77, k=14, 70 106 58 46 88 22

SPT(16)	1268809621754708513	0 8 50 68 120 140 194 198 236 240 294 314 366 384 426 434	-1218554459196
SPT(16)	1268810142051884143	0 24 64 66 76 78 84 136 288 340 346 348 358 360 400 424	-698257283566
SPT(16)	1268810467337962531	0 16 22 58 78 82 112 138 220 246 276 280 300 336 342 358	-372971205178
STPT(10)	1268810608779163361	0 2 6 8 18 20 30 32 36 38	-231530004348
SPT(18)	1268810664193391329	0 142 148 162 168 174 190 204 220 222 238 252 268 274 280 294 300 442	-176115776380
STPT(12)	1268810796161597231	0 2 6 8 48 50 138 140 180 182 186 188	-44147570478
SPT(20)	1268810872306770797	0 2 6 20 56 92 102 134 156 170 186 200 222 254 264 300 336 350 354 356	31997603088
SPT(16)	1268810968191034357	0 6 22 36 52 70 84 94 102 112 126 144 160 174 190 196	127881866648
STPT(10)	1268811410744561657	0 2 30 32 42 44 54 56 84 86	570435393948
SPT(16)	1268811696866993011	0 12 28 40 66 106 160 250 258 348 402 442 468 480 496 508	856557825302
STPT(10)	1268811889217831051	0 2 30 32 60 62 90 92 120 122	1048908663342