Prime p₀= 2159706341474570657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 22 2 64 2 88 2 70 2 (?)
a_n: 0 2 30 32 60 62 84 86 150 152 240 242 312 314
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: 314
Found by: Landjunge
db: batch=81, k=14, 28 28 22 64 88 70

SPT(16)	2159705588758192577	0 14 36 102 114 116 152 156 200 204 240 242 254 320 342 356	-752716378080
SPT(16)	2159705780913335129	0 24 54 60 72 74 144 212 222 290 360 362 374 380 410 434	-560561235528
TPT(14)	2159706086398850447	0 2 54 56 120 122 150 152 204 206 360 362 402 404	-255075720210
STPT(10)	2159706197798622827	0 2 12 14 72 74 132 134 144 146	-143675947830
SPT(16)	2159706214308395839	0 28 34 48 94 120 150 232 240 322 352 378 424 438 444 472	-127166174818
SPT(16)	2159706279939505811	0 56 78 90 120 122 140 156 272 288 306 308 338 350 372 428	-61535064846
STPT(10)	2159706543161788631	0 2 48 50 108 110 168 170 216 218	201687217974
STPT(10)	2159706756152600927	0 2 24 26 42 44 60 62 84 86	414678030270
SPT(16)	2159707020837995857	0 16 42 60 70 106 112 120 166 174 180 216 226 244 270 286	679363425200
SPT(16)	2159707582965404387	0 56 104 132 164 186 192 224 282 314 320 342 374 402 450 506	1241490833730
SPT(16)	2159708102454893989	0 34 40 48 64 102 154 160 342 348 400 438 454 462 468 502	1760980323332