Prime p₀= 2789758538701147889 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 28 2 4 2 40 2 46 2 (?)
a_n: 0 2 30 32 42 44 72 74 78 80 120 122 168 170
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: 170
Found by: UBT - Timbo
db: batch=82, k=14, 28 10 28 4 40 46

SPT(16)	2789757359312252743	0 16 58 64 78 84 108 196 318 406 430 436 450 456 498 514	-1179388895146
SPT(16)	2789757653168397479	0 24 60 68 102 128 152 168 194 210 234 260 294 302 338 362	-885532750410
SPT(18)	2789757687855222683	0 8 54 60 78 96 144 156 180 284 308 320 368 386 404 410 456 464	-850845925206
SPT(16)	2789757766690816513	0 16 34 40 64 114 148 180 184 216 250 300 324 330 348 364	-772010331376
STPT(10)	2789757956831917427	0 2 30 32 72 74 114 116 144 146	-581869230462
SPT(16)	2789758304966448253	0 28 54 58 118 124 154 210 214 270 300 306 366 370 396 424	-233734699636
STPT(10)	2789758931282507537	0 2 90 92 150 152 210 212 300 302	392581359648
SPT(16)	2789758970161786841	0 12 26 32 66 86 128 152 336 360 402 422 456 462 476 488	431460638952
STPT(10)	2789759521693517039	0 2 18 20 60 62 102 104 120 122	982992369150
SPT(16)	2789759671164941821	0 10 12 30 66 76 90 100 132 142 156 166 202 220 222 232	1132463793932
STPT(10)	2789760018519958997	0 2 60 62 102 104 144 146 204 206	1479818811108