Prime p₀= 2956903054001535017 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: ginga
db: batch=82, k=10, 2 28 2 10 2

STPT(10)	2956900031777653187	0 2 30 32 72 74 114 116 144 146	-3022223881830
STPT(12)	2956900552660478447	0 2 72 74 84 86 90 92 102 104 174 176	-2501341056570
SPT(16)	2956901075784675977	0 84 86 96 102 156 192 200 276 284 320 374 380 390 392 476	-1978216859040
TPT(14)	2956901782368334679	0 2 102 104 138 140 240 242 258 260 462 464 468 470	-1271633200338
SPT(16)	2956901785934167567	0 6 40 52 72 126 132 136 216 220 226 280 300 312 346 352	-1268067367450
TPT(14)	2956902863856671459	0 2 30 32 72 74 78 80 90 92 270 272 288 290	-190144863558
SPT(18)	2956903058135113531	0 16 22 30 42 90 96 126 198 250 322 352 358 406 418 426 432 448	4133578514
STPT(10)	2956903435529232071	0 2 36 38 78 80 120 122 156 158	381527697054
SPT(16)	2956903500940810723	0 18 24 54 130 144 186 208 276 298 340 354 430 460 466 484	446939275706
SPT(16)	2956903633926930421	0 16 42 52 66 82 100 112 126 138 156 172 186 196 222 238	579925395404
STPT(10)	2956903643976013481	0 2 36 38 78 80 120 122 156 158	589974478464