Prime p₀= 1296894624718234271 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 120 122 156 158
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: 158
Found by: Cruncher Pete
db: batch=77, k=10, 2 34 2 40 2

STPT(10)	1296893656847416709	0 2 12 14 90 92 168 170 180 182	-967870817562
SPT(16)	1296893823866581321	0 12 66 120 132 138 166 168 190 192 220 226 238 292 346 358	-800851652950
SPT(16)	1296893945111731583	0 14 44 56 86 114 134 180 200 246 266 294 324 336 366 380	-679606502688
SPT(16)	1296893970077899373	0 38 56 66 74 108 144 168 206 230 266 300 308 318 336 374	-654640334898
SPT(16)	1296894330525370019	0 14 24 72 84 104 114 132 182 200 210 230 242 290 300 314	-294192864252
TPT(14)	1296894577466171237	0 2 12 14 24 26 30 32 114 116 222 224 294 296	-47252063034
STPT(10)	1296894659731450457	0 2 30 32 42 44 54 56 84 86	35013216186
STPT(12)	1296894700238370587	0 2 12 14 54 56 90 92 132 134 144 146	75520136316
SPT(16)	1296894957177096281	0 2 12 26 56 86 90 92 96 98 102 132 162 176 186 188	332458862010
SPT(16)	1296894994273196959	0 40 42 64 78 112 138 172 180 214 240 274 288 310 312 352	369554962688
STPT(10)	1296895512806960291	0 2 36 38 78 80 120 122 156 158	888088726020