Prime p₀= 1295367760448403881 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 82 2 154 2 28 2 40 2 10 2 (?)
a_n: 0 2 66 68 150 152 306 308 336 338 378 380 390 392
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: 392
Found by: Cruncher Pete
db: batch=77, k=14, 64 82 154 28 40 10

SPT(16)	1295365969761760301	0 20 30 72 116 138 140 170 198 228 230 252 296 338 348 368	-1790686643580
TPT(14)	1295366177536363547	0 2 30 32 42 44 60 62 84 86 102 104 234 236	-1582912040334
SPT(16)	1295366713882387369	0 4 28 60 70 144 168 174 238 244 268 342 352 384 408 412	-1046566016512
SPT(16)	1295367251905347809	0 60 62 104 140 182 192 198 284 290 300 342 378 420 422 482	-508543056072
SPT(16)	1295367438653701723	0 16 18 24 66 88 150 190 234 274 336 358 400 406 408 424	-321794702158
SPT(16)	1295367583524270133	0 30 96 100 124 160 204 216 274 286 330 366 390 394 460 490	-176924133748
TPT(14)	1295367940317010667	0 2 42 44 72 74 84 86 120 122 162 164 174 176	179868606786
SPT(16)	1295368289338117051	0 22 30 66 148 168 198 208 210 220 250 270 352 388 396 418	528889713170
SPT(16)	1295368392890313541	0 42 46 66 112 130 252 268 270 286 408 426 472 492 496 538	632441909660
SPT(16)	1295368469387534389	0 12 18 52 70 84 94 102 130 138 148 162 180 214 220 232	708939130508
TPT(14)	1295368471951949357	0 2 30 32 144 146 222 224 252 254 282 284 294 296	711503545476