Prime p₀= 958435985652252377 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 52 2 28 2 64 2 28 2 130 2 (?)
a_n: 0 2 30 32 84 86 114 116 180 182 210 212 342 344
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: HenkM
db: batch=76, k=14, 28 52 28 64 28 130

SPT(16)	958434622910984171	0 8 30 96 122 128 162 192 266 296 330 336 362 428 450 458	-1362741268206
SPT(16)	958434842915406497	0 6 12 36 72 86 182 266 420 504 600 614 650 674 680 686	-1142736845880
STPT(10)	958434993273279491	0 2 156 158 168 170 180 182 336 338	-992378972886
SPT(16)	958435635195698111	0 6 36 102 138 168 200 228 260 288 320 350 386 452 482 488	-350456554266
SPT(16)	958435856006956031	0 38 42 92 96 110 132 152 246 266 288 302 306 356 360 398	-129645296346
STPT(10)	958435887569231681	0 2 30 32 78 80 126 128 156 158	-98083020696
SPT(16)	958436255622703639	0 12 40 82 88 144 172 190 192 210 238 294 300 342 370 382	269970451262
STPT(10)	958436430747626627	0 2 30 32 42 44 54 56 84 86	445095374250
SPT(20)	958436605450065901	0 66 70 90 102 118 148 190 222 232 276 286 318 360 390 406 418 438 442 508	619797813524
STPT(10)	958436612587863527	0 2 24 26 42 44 60 62 84 86	626935611150
TPT(14)	958437132367458281	0 2 30 32 126 128 150 152 156 158 168 170 180 182	1146715205904