Prime p₀= 2778190844463793007 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 58 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 132 134 144 146
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: 146
Found by: Roadranner
db: batch=82, k=10, 2 10 2 58 2

SPT(16)	2778189944340250493	0 6 26 48 56 104 110 114 170 174 180 228 236 258 278 284	-900123542514
SPT(16)	2778189976193075099	0 18 74 78 102 110 144 174 188 218 252 260 284 288 344 362	-868270717908
STPT(10)	2778190134520503881	0 2 6 8 48 50 90 92 96 98	-709943289126
SPT(16)	2778190240171165381	0 30 72 102 126 156 162 178 210 226 232 262 286 316 358 388	-604292627626
SPT(16)	2778190563942540841	0 6 22 30 40 48 78 96 142 160 190 198 208 216 232 238	-280521252166
SPT(16)	2778190566593860273	0 10 70 78 94 160 190 196 198 204 234 300 316 324 384 394	-277869932734
STPT(10)	2778190954286719589	0 2 48 50 60 62 72 74 120 122	109822926582
STPT(10)	2778190973020427927	0 2 30 32 42 44 54 56 84 86	128556634920
SPT(16)	2778191366662512991	0 10 42 58 78 88 112 126 172 186 210 220 240 256 288 298	522198719984
SPT(16)	2778191757791137081	0 42 70 72 76 78 108 132 136 160 190 192 196 198 226 268	913327344074
STPT(10)	2778192084157021289	0 2 18 20 30 32 42 44 60 62	1239693228282