Prime p₀= 2712796783352205617 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)	2712796276666113223	0 6 40 66 76 148 166 238 258 330 348 420 430 456 490 496	-506686092394
SPT(16)	2712796375615689457	0 12 22 24 42 64 70 76 240 246 252 274 292 294 304 316	-407736516160
SPT(16)	2712796488078578173	0 34 70 84 126 154 180 184 210 214 240 268 310 324 360 394	-295273627444
STPT(10)	2712796535428020827	0 2 30 32 60 62 90 92 120 122	-247924184790
STPT(10)	2712796589991374021	0 2 36 38 78 80 120 122 156 158	-193360831596
SPT(16)	2712796644474836527	0 10 46 66 82 102 112 130 132 150 160 180 196 216 252 262	-138877369090
STPT(10)	2712797004871748657	0 2 90 92 210 212 330 332 420 422	221519543040
SPT(16)	2712797124352221553	0 6 40 64 66 114 136 190 210 264 286 334 336 360 394 400	341000015936
STPT(10)	2712797862871433537	0 2 30 32 72 74 114 116 144 146	1079519227920
STPT(10)	2712798119250884837	0 2 30 32 42 44 54 56 84 86	1335898679220
STPT(10)	2712798545143336619	0 2 12 14 30 32 48 50 60 62	1761791131002