Prime p₀= 1126650768229522301 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 76 2 28 2 28 2 76 2 (?)
a_n: 0 2 78 80 108 110 138 140 216 218
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: 218
Found by: crashtech
db: batch=76, k=10, 2 76 2 28 2

SPT(16)	1126649202860744869	0 88 102 208 238 270 280 304 348 372 382 414 444 550 564 652	-1565368777432
SPT(16)	1126649359212599501	0 6 12 42 48 56 96 122 126 152 192 200 206 236 242 248	-1409016922800
SPT(16)	1126649633485547851	0 12 70 78 120 138 150 166 252 268 280 298 340 348 406 418	-1134743974450
STPT(10)	1126649703957007331	0 2 6 8 48 50 90 92 96 98	-1064272514970
STPT(10)	1126650216111443237	0 2 30 32 42 44 54 56 84 86	-552118079064
STPT(10)	1126650541819023899	0 2 18 20 30 32 42 44 60 62	-226410498402
SPT(16)	1126651131850828127	0 20 32 90 180 216 224 302 354 432 440 476 566 624 636 656	363621305826
SPT(16)	1126651609308797443	0 6 46 60 100 120 156 174 226 244 280 300 340 354 394 400	841079275142
STPT(12)	1126652175463846439	0 2 18 20 42 44 48 50 72 74 90 92	1407234324138
STPT(10)	1126652179795055201	0 2 36 38 78 80 120 122 156 158	1411565532900
TPT(14)	1126652537255885669	0 2 42 44 78 80 162 164 198 200 252 254 330 332	1769026363368