Prime p₀= 3833896687517354999 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 70 2 76 2 76 2 10 2 40 2 (?)
a_n: 0 2 60 62 132 134 210 212 288 290 300 302 342 344
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: 344
Found by: DGPickett
db: batch=84, k=14, 58 70 76 76 10 40

SPT(18)	3833895110078129633	0 6 36 78 98 120 174 210 218 276 284 320 374 396 416 458 488 494	-1577439225366
TPT(14)	3833895125331924767	0 2 30 32 90 92 114 116 162 164 210 212 294 296	-1562185430232
SPT(16)	3833895426527065667	0 14 32 74 102 110 120 144 182 206 216 224 252 294 312 326	-1260990289332
SPT(16)	3833895525144245441	0 2 6 20 30 72 86 90 122 126 140 182 192 206 210 212	-1162373109558
SPT(16)	3833896079587257337	0 10 30 76 82 106 114 142 174 202 210 234 240 286 306 316	-607930097662
STPT(10)	3833896414493727467	0 2 30 32 42 44 54 56 84 86	-273023627532
TPT(14)	3833896750346398607	0 2 102 104 132 134 240 242 312 314 390 392 474 476	62829043608
SPT(16)	3833897467434441157	0 64 66 70 100 106 150 156 280 286 330 336 366 370 372 436	779917086158
SPT(16)	3833897812047109379	0 48 62 68 122 144 150 152 180 182 188 210 264 270 284 332	1124529754380
TPT(14)	3833899123217260397	0 2 42 44 60 62 222 224 252 254 282 284 312 314	2435699905398
STPT(10)	3833899260607946597	0 2 12 14 42 44 72 74 84 86	2573090591598