Prime p₀= 2506381347276351287 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: Ben
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2506379923100646793	0 6 16 84 88 90 96 100 144 148 154 156 160 228 238 244	-1424175704494
SPT(16)	2506380245460928691	0 8 32 92 110 152 158 228 320 390 396 438 456 516 540 548	-1101815422596
SPT(16)	2506380508958421269	0 12 18 32 42 54 108 144 278 314 368 380 390 404 410 422	-838317930018
TPT(14)	2506380660532794467	0 2 30 32 42 44 90 92 120 122 132 134 210 212	-686743556820
STPT(10)	2506380792774678641	0 2 6 8 48 50 90 92 96 98	-554501672646
SPT(16)	2506381225191181193	0 6 30 36 38 84 104 114 140 150 170 216 218 224 248 254	-122085170094
TPT(14)	2506381747852529639	0 2 30 32 78 80 120 122 180 182 198 200 210 212	400576178352
SPT(16)	2506381998331411283	0 14 20 30 54 110 114 128 366 380 384 440 464 474 480 494	651055059996
STPT(10)	2506382389402938647	0 2 12 14 42 44 72 74 84 86	1042126587360
SPT(16)	2506382534782041337	0 22 30 64 112 126 132 156 160 184 190 204 252 286 294 316	1187505690050
SPT(16)	2506382796304955717	0 14 30 56 92 114 140 162 224 246 272 294 330 356 372 386	1449028604430