Prime p₀= 2566822936245452537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 100 2 28 2 28 2 34 2 (?)
a_n: 0 2 30 32 42 44 144 146 174 176 204 206 240 242
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: 242
Found by: JayPi
db: batch=82, k=14, 28 10 100 28 28 34

SPT(13)	2566822227162763813	0 18 48 60 90 144 174 204 258 288 300 330 348	-709082688724
SPT(16)	2566822356516556979	0 8 12 24 38 42 54 74 78 98 110 114 128 140 144 152	-579728895558
STPT(10)	2566822386970254617	0 2 12 14 42 44 72 74 84 86	-549275197920
SPT(16)	2566822418201772587	0 50 86 96 114 126 134 156 314 336 344 356 374 384 420 470	-518043679950
STPT(10)	2566822579025171651	0 2 30 32 60 62 90 92 120 122	-357220280886
STPT(10)	2566822917317480579	0 2 18 20 30 32 42 44 60 62	-18927971958
STPT(10)	2566823100556073927	0 2 12 14 42 44 72 74 84 86	164310621390
STPT(10)	2566823472576492341	0 2 36 38 78 80 120 122 156 158	536331039804
SPT(16)	2566823505522712523	0 6 20 98 120 150 218 230 324 336 404 434 456 534 548 554	569277259986
SPT(16)	2566824310975730159	0 2 30 74 78 90 102 120 182 200 212 224 228 272 300 302	1374730277622
SPT(16)	2566824370837090537	0 6 40 42 54 66 76 90 196 210 220 232 244 246 280 286	1434591638000