Prime p₀= 2686262201239003061 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 40 2 166 2 28 2 220 2 (?)
a_n: 0 2 36 38 78 80 120 122 288 290 318 320 540 542
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: 542
Found by: RFGuy_KCCO
db: batch=82, k=14, 34 40 40 166 28 220

SPT(16)	2686260885090846929	0 12 32 62 78 84 90 104 138 152 158 164 180 210 230 242	-1316148156132
STPT(10)	2686261308101755169	0 2 42 44 60 62 78 80 120 122	-893137247892
STPT(10)	2686261505637182621	0 2 30 32 78 80 126 128 156 158	-695601820440
SPT(16)	2686261747372284149	0 8 14 18 48 60 78 98 210 230 248 260 290 294 300 308	-453866718912
STPT(10)	2686262092634201759	0 2 18 20 30 32 42 44 60 62	-108604801302
STPT(10)	2686262157068239439	0 2 18 20 30 32 42 44 60 62	-44170763622
SPT(16)	2686262569087842211	0 22 52 70 78 90 126 136 192 202 238 250 258 276 306 328	367848839150
SPT(16)	2686262746070791639	0 12 42 82 90 100 124 154 168 198 222 232 240 280 310 322	544831788578
STPT(12)	2686263390360693329	0 2 30 32 42 44 90 92 102 104 132 134	1189121690268
TPT(14)	2686263674201325509	0 2 12 14 18 20 30 32 90 92 168 170 222 224	1472962322448
SPT(16)	2686263732889232207	0 6 20 62 66 122 140 152 174 186 204 260 264 306 320 326	1531650229146