Prime p₀= 2303058230959757657 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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: Orange Kid
db: batch=81, k=10, 2 10 2 28 2

STPT(12)	2303056681963780187	0 2 12 14 42 44 102 104 132 134 144 146	-1548995977470
SPT(16)	2303057089719551881	0 36 46 88 108 130 132 190 198 256 258 280 300 342 352 388	-1141240205776
SPT(16)	2303057504571582683	0 44 68 134 138 156 198 228 236 266 308 326 330 396 420 464	-726388174974
STPT(10)	2303057837684987561	0 2 6 8 48 50 90 92 96 98	-393274770096
STPT(10)	2303057993453031509	0 2 30 32 60 62 90 92 120 122	-237506726148
STPT(10)	2303058068236013321	0 2 36 38 78 80 120 122 156 158	-162723744336
SPT(16)	2303058311780743729	0 84 88 144 172 210 232 234 238 240 262 300 328 384 388 472	80820986072
STPT(10)	2303058327945010817	0 2 24 26 42 44 60 62 84 86	96985253160
SPT(16)	2303058459963635461	0 40 58 72 112 142 150 162 196 208 216 246 286 300 318 358	229003877804
SPT(16)	2303058798696977429	0 38 42 78 84 92 110 128 174 192 210 218 224 260 264 302	567737219772
STPT(10)	2303059647839863709	0 2 18 20 30 32 42 44 60 62	1416880106052