Prime p₀= 1268571257993344307 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 154 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 114 116 270 272 300 302 312 314 324 326 354 356
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: 356
Found by: Megacruncher
db: batch=77, k=14, 112 154 28 10 10 28

SPT(16)	1268570321255097409	0 52 58 72 148 150 162 174 178 190 202 204 280 294 300 352	-936738246898
STPT(10)	1268570414629768709	0 2 18 20 30 32 42 44 60 62	-843363575598
STPT(10)	1268570461678308959	0 2 18 20 30 32 42 44 60 62	-796315035348
TPT(14)	1268570505050493779	0 2 30 32 78 80 120 122 162 164 180 182 222 224	-752942850528
SPT(16)	1268570858120057251	0 28 42 88 96 100 102 130 138 166 168 172 180 226 240 268	-399873287056
SPT(16)	1268570876325864641	0 38 66 80 98 110 116 158 168 210 216 228 246 260 288 326	-381667479666
STPT(10)	1268571257993344577	0 2 30 32 42 44 54 56 84 86	270
SPT(16)	1268571731896528027	0 24 64 70 90 132 174 202 282 310 352 394 414 420 460 484	473903183720
SPT(16)	1268572146246750193	0 24 28 58 70 76 84 90 214 220 228 234 246 276 280 304	888253405886
SPT(16)	1268572314166893539	0 18 42 48 62 90 102 128 294 320 332 360 374 380 404 422	1056173549232
SPT(16)	1268572532198547941	0 8 30 56 78 120 162 176 192 206 248 290 312 338 360 368	1274205203634