Prime p₀= 4364179760056253171 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 16 2 22 2 28 2 124 2 (?)
a_n: 0 2 66 68 108 110 126 128 150 152 180 182 306 308
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: 308
Found by: Autofuzzy
db: batch=85, k=14, 64 40 16 22 28 124

TPT(14)	4364178486353055659	0 2 42 44 48 50 78 80 120 122 132 134 168 170	-1273703197512
SPT(16)	4364178517101457363	0 24 30 36 46 58 60 64 150 154 156 168 178 184 190 214	-1242954795808
SPT(16)	4364178616741423621	0 16 36 42 60 82 126 130 138 142 186 208 226 232 252 268	-1143314829550
STPT(10)	4364178929531321777	0 2 30 32 60 62 90 92 120 122	-830524931394
SPT(18)	4364179063305226247	0 36 84 90 104 132 134 140 162 164 186 192 194 222 236 242 290 326	-696751026924
SPT(16)	4364179462237786717	0 16 54 66 70 96 114 120 130 136 154 180 184 196 234 250	-297818466454
TPT(14)	4364179780088374451	0 2 18 20 30 32 168 170 186 188 228 230 258 260	20032121280
STPT(10)	4364180028394541627	0 2 24 26 42 44 60 62 84 86	268338288456
SPT(16)	4364180948574685739	0 30 44 54 78 90 92 114 158 180 182 194 218 228 242 272	1188518432568
SPT(16)	4364181808888502131	0 58 60 66 70 72 100 102 136 138 166 168 172 178 180 238	2048832248960
STPT(10)	4364182468333483067	0 2 30 32 42 44 54 56 84 86	2708277229896