Prime p₀= 1296894659731450457 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: Cruncher Pete
db: batch=77, k=10, 2 28 2 10 2

SPT(16)	1296893823866581321	0 12 66 120 132 138 166 168 190 192 220 226 238 292 346 358	-835864869136
SPT(16)	1296893945111731583	0 14 44 56 86 114 134 180 200 246 266 294 324 336 366 380	-714619718874
SPT(16)	1296893970077899373	0 38 56 66 74 108 144 168 206 230 266 300 308 318 336 374	-689653551084
SPT(16)	1296894330525370019	0 14 24 72 84 104 114 132 182 200 210 230 242 290 300 314	-329206080438
TPT(14)	1296894577466171237	0 2 12 14 24 26 30 32 114 116 222 224 294 296	-82265279220
STPT(10)	1296894624718234271	0 2 36 38 78 80 120 122 156 158	-35013216186
STPT(12)	1296894700238370587	0 2 12 14 54 56 90 92 132 134 144 146	40506920130
SPT(16)	1296894957177096281	0 2 12 26 56 86 90 92 96 98 102 132 162 176 186 188	297445645824
SPT(16)	1296894994273196959	0 40 42 64 78 112 138 172 180 214 240 274 288 310 312 352	334541746502
STPT(10)	1296895512806960291	0 2 36 38 78 80 120 122 156 158	853075509834
SPT(16)	1296895872878259691	0 70 78 148 160 168 202 300 310 408 442 450 462 532 540 610	1213146809234