Prime p₀= 2858223130944376211 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 106 2 82 2 16 2 28 2 106 2 (?)
a_n: 0 2 18 20 126 128 210 212 228 230 258 260 366 368
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: Ben
db: batch=82, k=14, 16 106 82 16 28 106

STPT(10)	2858221118430461237	0 2 24 26 42 44 60 62 84 86	-2012513914974
STPT(10)	2858221313030266607	0 2 54 56 72 74 90 92 144 146	-1817914109604
SPT(16)	2858222230392040469	0 48 72 90 114 122 128 132 140 144 150 158 182 200 224 272	-900552335742
SPT(16)	2858222902140368717	0 12 36 44 66 122 146 174 212 240 264 320 342 350 374 386	-228804007494
SPT(16)	2858222910824189719	0 4 12 40 52 54 90 130 132 172 208 210 222 250 258 262	-220120186492
STPT(10)	2858222949156467237	0 2 42 44 72 74 102 104 144 146	-181787908974
STPT(10)	2858223183482021627	0 2 30 32 42 44 54 56 84 86	52537645416
STPT(10)	2858223267994940939	0 2 42 44 120 122 198 200 240 242	137050564728
STPT(10)	2858223577082721047	0 2 30 32 72 74 114 116 144 146	446138344836
SPT(16)	2858224450592958319	0 12 22 52 124 160 162 190 222 250 252 288 360 390 400 412	1319648582108
SPT(16)	2858224516072779551	0 26 96 120 126 152 210 222 260 272 330 356 362 386 456 482	1385128403340