Prime p₀= 2956342702486262819 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 226 2 142 2 4 2 118 2 40 2 118 2 (?)
a_n: 0 2 228 230 372 374 378 380 498 500 540 542 660 662
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: 662
Found by: MarkRBright
db: batch=82, k=14, 226 142 4 118 40 118

SPT(16)	2956341553839226037	0 44 90 134 176 200 216 240 260 284 300 324 366 410 456 500	-1148647036782
SPT(16)	2956341755702464471	0 40 66 82 88 102 130 168 220 258 286 300 306 322 348 388	-946783798348
SPT(16)	2956341857891563223	0 8 54 68 78 140 176 216 278 318 354 416 426 440 486 494	-844594699596
STPT(10)	2956342255089736991	0 2 30 32 78 80 126 128 156 158	-447396525828
SPT(16)	2956342300214468467	0 4 30 64 96 186 196 214 222 240 250 340 372 406 432 436	-402271794352
STPT(10)	2956342630098117311	0 2 6 8 18 20 30 32 36 38	-72388145508
STPT(10)	2956342736399599367	0 2 60 62 72 74 84 86 144 146	33913336548
TPT(16)	2956342918125462641	0 2 96 98 138 140 150 152 156 158 276 278 360 362 378 380	215639199822
STPT(10)	2956343423727508457	0 2 30 32 42 44 54 56 84 86	721241245638
STPT(10)	2956343665235097419	0 2 18 20 60 62 102 104 120 122	962748834600
SPT(16)	2956343812684299497	0 26 42 126 146 152 174 260 276 362 384 390 410 494 510 536	1110198036678