Prime p₀= 1286415944476201841 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 46 2 160 2 28 2 46 2 (?)
a_n: 0 2 66 68 78 80 126 128 288 290 318 320 366 368
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: 368
Found by: Cruncher Pete
db: batch=77, k=14, 64 10 46 160 28 46

SPT(16)	1286414849505889897	0 24 54 72 96 114 124 166 180 222 232 250 274 292 322 346	-1094970311944
SPT(16)	1286415059571081107	0 6 30 44 62 66 122 132 314 324 380 384 402 416 440 446	-884905120734
STPT(10)	1286415282697080449	0 2 12 14 90 92 168 170 180 182	-661779121392
SPT(16)	1286415415059404621	0 90 102 122 132 140 150 186 206 242 252 260 270 290 302 392	-529416797220
STPT(10)	1286415659494674617	0 2 30 32 42 44 54 56 84 86	-284981527224
STPT(10)	1286415704654198717	0 2 30 32 42 44 54 56 84 86	-239822003124
SPT(16)	1286416112571639983	0 36 66 86 104 114 128 150 194 216 230 240 258 278 308 344	168095438142
SPT(16)	1286416190866901473	0 30 36 46 54 96 106 136 198 228 238 280 288 298 304 334	246390699632
TPT(14)	1286416601442444917	0 2 54 56 174 176 300 302 354 356 474 476 564 566	656966243076
SPT(16)	1286416696281353867	0 20 72 116 150 170 272 300 332 360 462 482 516 560 612 632	751805152026
SPT(16)	1286416792510078571	0 2 66 68 80 86 110 128 150 168 192 198 210 212 276 278	848033876730