Prime p₀= 935872542007027967 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 40 2 124 2 28 2 70 2 (?)
a_n: 0 2 12 14 42 44 84 86 210 212 240 242 312 314
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: 314
Found by: gemini8
db: batch=76, k=14, 10 28 40 124 28 70

SPT(16)	935871781398550201	0 28 36 78 102 130 150 156 232 238 258 286 310 352 360 388	-760608477766
SPT(16)	935871817795817563	0 6 40 90 150 156 178 180 196 198 220 226 286 336 370 376	-724211210404
SPT(16)	935871997888064921	0 8 32 120 158 168 192 206 222 236 260 270 308 396 420 428	-544118963046
SPT(16)	935872046341567817	0 14 32 42 60 66 104 146 150 192 230 236 254 264 282 296	-495665460150
STPT(10)	935872303370252819	0 2 18 20 30 32 42 44 60 62	-238636775148
SPT(16)	935872437337792543	0 24 46 70 88 108 156 186 238 268 316 336 354 378 400 424	-104669235424
STPT(12)	935872605042497537	0 2 42 44 60 62 114 116 132 134 174 176	63035469570
SPT(16)	935872607294447897	0 2 42 54 60 74 116 140 156 180 222 236 242 254 294 296	65287419930
STPT(10)	935872646256960077	0 2 30 32 42 44 54 56 84 86	104249932110
SPT(16)	935872648480498009	0 4 30 64 84 102 114 120 172 178 190 208 228 262 288 292	106473470042
STPT(10)	935872739533656479	0 2 18 20 60 62 102 104 120 122	197526628512