Prime p₀= 974544974541502457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 28 2 52 2 28 2 34 2 (?)
a_n: 0 2 30 32 60 62 90 92 144 146 174 176 210 212
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: 212
Found by: HenkM
db: batch=76, k=14, 28 28 28 52 28 34

SPT(16)	974543557513100923	0 24 60 64 66 106 204 210 424 430 528 568 570 574 610 634	-1417028401534
SPT(16)	974544007702525679	0 30 80 144 150 174 188 200 222 234 248 272 278 342 392 422	-966838976778
SPT(16)	974544126615997537	0 4 10 36 52 150 190 202 204 216 256 354 370 396 402 406	-847925504920
SPT(16)	974544379638173021	0 42 68 80 116 126 138 140 168 170 182 192 228 240 266 308	-594903329436
SPT(16)	974544542515879739	0 18 32 42 48 50 78 84 98 104 132 134 140 150 164 182	-432025622718
STPT(10)	974544915699917447	0 2 12 14 72 74 132 134 144 146	-58841585010
STPT(10)	974545017537341177	0 2 42 44 72 74 102 104 144 146	42995838720
SPT(16)	974545033077384469	0 24 30 120 130 142 150 154 180 184 192 204 214 304 310 334	58535882012
STPT(10)	974545049959834037	0 2 24 26 42 44 60 62 84 86	75418331580
STPT(10)	974545222164191141	0 2 36 38 78 80 120 122 156 158	247622688684
STPT(10)	974545271713855481	0 2 6 8 48 50 90 92 96 98	297172353024