Prime p₀= 1369826616649906157 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 84 86
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 86
Found by: emoga
db: batch=77, k=10, 2 10 2 28 2

SPT(16)	1369824807341888839	0 34 40 54 90 100 130 138 160 168 198 208 244 258 264 298	-1809308017318
SPT(16)	1369825026624820763	0 18 44 86 104 114 138 156 158 176 200 210 228 270 296 314	-1590025085394
SPT(16)	1369825294470876479	0 12 60 134 144 150 174 230 264 320 344 350 360 434 482 494	-1322179029678
STPT(10)	1369825364426372597	0 2 42 44 102 104 162 164 204 206	-1252223533560
SPT(20)	1369825402469202323	0 8 14 56 66 86 98 140 170 176 228 234 264 306 318 338 348 390 396 404	-1214180703834
SPT(16)	1369825436352997451	0 50 60 66 80 98 116 120 128 132 150 168 182 188 198 248	-1180296908706
STPT(10)	1369826813710516457	0 2 30 32 102 104 174 176 204 206	197060610300
TPT(14)	1369827140212647227	0 2 180 182 234 236 354 356 390 392 402 404 432 434	523562741070
SPT(16)	1369827583047615961	0 10 12 36 78 120 142 148 240 246 268 310 352 376 378 388	966397709804
TPT(14)	1369827641392499699	0 2 18 20 42 44 168 170 252 254 312 314 378 380	1024742593542
STPT(10)	1369827778057939799	0 2 18 20 30 32 42 44 60 62	1161408033642