Prime p₀= 2836429920290245967 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 70 2 58 2 208 2 64 2 88 2 (?)
a_n: 0 2 42 44 114 116 174 176 384 386 450 452 540 542
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: 542
Found by: Landjunge
db: batch=82, k=14, 40 70 58 208 64 88

SPT(16)	2836426680684784931	0 20 32 156 176 260 276 302 366 392 408 492 512 636 648 668	-3239605461036
SPT(16)	2836427314120143257	0 12 26 50 54 96 104 182 204 282 290 332 336 360 374 386	-2606170102710
STPT(10)	2836427487728674517	0 2 60 62 72 74 84 86 144 146	-2432561571450
SPT(16)	2836428621331199831	0 6 18 26 30 32 48 62 66 80 96 98 102 110 122 128	-1298959046136
SPT(16)	2836428637078533437	0 12 42 90 110 210 240 276 296 332 362 462 482 530 560 572	-1283211712530
SPT(16)	2836428964236239341	0 12 16 28 48 82 118 132 166 180 216 250 270 282 286 298	-956054006626
STPT(10)	2836430014789219481	0 2 6 8 48 50 90 92 96 98	94498973514
SPT(16)	2836430174349650987	0 20 62 72 80 120 132 146 150 164 176 216 224 234 276 296	254059405020
SPT(16)	2836430245312712417	0 20 26 50 90 92 120 122 150 152 180 182 222 246 252 272	325022466450
SPT(16)	2836430265157436359	0 10 40 84 174 178 198 208 210 220 240 244 334 378 408 418	344867190392
STPT(10)	2836430434729303637	0 2 30 32 42 44 54 56 84 86	514439057670