Prime p₀= 2305021781296439501 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: Orange Kid
db: batch=81, k=10, 2 4 2 10 2

STPT(12)	2305020849744294359	0 2 18 20 72 74 138 140 192 194 210 212	-931552145142
STPT(10)	2305020975501181841	0 2 36 38 78 80 120 122 156 158	-805795257660
SPT(20)	2305021013050486331	0 12 56 86 128 168 252 258 350 368 390 408 500 506 590 630 672 702 746 758	-768245953170
SPT(16)	2305021043665373947	0 16 40 46 64 96 114 132 154 172 190 222 240 246 270 286	-737631065554
STPT(10)	2305021555663776797	0 2 12 14 42 44 72 74 84 86	-225632662704
SPT(16)	2305021730167495813	0 18 28 88 90 130 138 154 234 250 258 298 300 360 370 388	-51128943688
SPT(16)	2305022404507361797	0 10 16 24 30 42 46 52 144 150 154 166 172 180 186 196	623210922296
STPT(10)	2305022429715853667	0 2 30 32 42 44 54 56 84 86	648419414166
STPT(10)	2305022446239278747	0 2 114 116 282 284 450 452 564 566	664942839246
SPT(16)	2305022557062191069	0 20 32 42 54 104 134 158 204 228 258 308 320 330 342 362	775765751568
SPT(16)	2305023228971775727	0 6 30 52 60 64 106 142 204 240 282 286 294 316 340 346	1447675336226