Prime p₀= 1296900189788604221 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: Cruncher Pete
db: batch=77, k=10, 2 4 2 10 2

STPT(10)	1296898928744926019	0 2 42 44 60 62 78 80 120 122	-1261043678202
SPT(16)	1296898956766155593	0 6 48 78 86 120 134 158 186 210 224 258 266 296 338 344	-1233022448628
SPT(16)	1296899141646771281	0 2 42 68 86 92 126 132 176 182 216 222 240 266 306 308	-1048141832940
SPT(13)	1296899562812054323	0 30 36 78 90 96 168 240 246 258 300 306 336	-626976549898
STPT(10)	1296899753394244157	0 2 54 56 72 74 90 92 144 146	-436394360064
SPT(16)	1296899885509355279	0 14 50 60 62 104 152 168 194 210 258 300 302 312 348 362	-304279248942
SPT(16)	1296901021037034013	0 24 76 84 90 210 234 238 276 280 304 424 430 438 490 514	831248429792
STPT(12)	1296901116141277637	0 2 42 44 84 86 90 92 132 134 174 176	926352673416
STPT(10)	1296901193514153011	0 2 36 38 78 80 120 122 156 158	1003725548790
STPT(10)	1296901514818976189	0 2 12 14 30 32 48 50 60 62	1325030371968
TPT(14)	1296901951665130901	0 2 30 32 60 62 138 140 156 158 198 200 276 278	1761876526680