Prime p₀= 2116678287353631317 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: Vato
db: batch=80, k=10, 2 28 2 10 2

STPT(10)	2116676488249366661	0 2 36 38 78 80 120 122 156 158	-1799104264656
STPT(10)	2116676532934233167	0 2 60 62 72 74 84 86 144 146	-1754419398150
SPT(16)	2116676566819419167	0 30 36 132 146 170 180 182 210 212 222 246 260 356 362 392	-1720534212150
SPT(16)	2116676626406566111	0 70 76 90 96 136 186 192 280 286 336 376 382 396 402 472	-1660947065206
SPT(16)	2116677005870769707	0 14 24 56 60 92 96 102 134 140 144 176 180 212 222 236	-1281482861610
SPT(20)	2116677967659698227	0 16 52 64 70 100 102 124 142 154 222 234 252 274 276 306 312 324 360 376	-319693933090
STPT(10)	2116678404680738537	0 2 60 62 72 74 84 86 144 146	117327107220
TPT(14)	2116679288857164737	0 2 12 14 30 32 54 56 114 116 144 146 210 212	1001503533420
STPT(10)	2116679382501204791	0 2 6 8 48 50 90 92 96 98	1095147573474
STPT(10)	2116679383899988091	0 2 30 32 60 62 90 92 120 122	1096546356774
SPT(16)	2116679437185532831	0 42 148 150 156 162 190 192 196 198 226 232 238 240 346 388	1149831901514