Prime p₀= 84556508596966589 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 28 2 10 2 (?)
a_n: 0 2 30 32 42 44 72 74 78 80 108 110 120 122
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: 122
Found by: [SG-2W]Kurzer
db: batch=67, k=14, 28 10 28 4 28 10

SPT(14)	84556433134698179	0 2 42 72 74 92 114 158 180 198 200 230 270 272	-75462268410
SPT(14)	84556437661190837	0 2 14 30 56 60 66 80 86 90 116 132 144 146	-70935775752
SPT(14)	84556486161239621	0 2 20 42 60 68 158 240 330 338 356 378 396 398	-22435726968
TPT(12)	84556491425988077	0 2 12 14 42 44 60 62 114 116 210 212	-17170978512
SPT(16)	84556500277148989	0 40 60 70 94 112 162 192 250 280 330 348 372 382 402 442	-8319817600
SPT(14)	84556507664348449	0 42 108 132 190 210 228 262 280 300 358 382 448 490	-932618140
STPT(12)	84556508596966619	0 2 12 14 42 44 48 50 78 80 90 92	30
SPT(14)	84556522762318627	0 4 12 40 42 82 130 216 264 304 306 334 342 346	14165352038
SPT(16)	84556526043923621	0 8 36 78 86 108 120 146 270 296 308 330 338 380 408 416	17446957032
SPT(14)	84556531923992473	0 46 64 70 78 90 120 154 184 196 204 210 228 274	23327025884
SPT(14)	84556536290306543	0 30 38 60 80 114 116 168 170 204 224 246 254 284	27693339954