Prime p₀= 2317499997193666457 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: Coleslaw
db: batch=81, k=10, 2 28 2 10 2

SPT(16)	2317497754877062963	0 90 106 108 168 244 280 294 310 324 360 436 496 498 514 604	-2242316603494
SPT(13)	2317497901530245831	0 48 60 96 108 126 138 150 168 180 216 228 276	-2095663420626
SPT(16)	2317498280141118287	0 6 12 14 20 42 56 66 80 90 104 126 132 134 140 146	-1717052548170
STPT(10)	2317498935316956497	0 2 30 32 42 44 54 56 84 86	-1061876709960
SPT(16)	2317499363593572527	0 42 96 116 146 162 176 200 252 276 290 306 336 356 410 452	-633600093930
SPT(16)	2317499643054406583	0 38 56 78 90 108 216 240 266 290 398 416 428 450 468 506	-354139259874
TPT(14)	2317500289688603267	0 2 54 56 84 86 132 134 162 164 174 176 210 212	292494936810
STPT(10)	2317500347355672077	0 2 30 32 42 44 54 56 84 86	350162005620
SPT(16)	2317501015296059311	0 46 82 108 130 132 162 186 322 346 376 378 400 426 462 508	1018102392854
SPT(16)	2317501183380234097	0 82 94 96 100 112 114 156 250 292 294 306 310 312 324 406	1186186567640
SPT(16)	2317501240176198229	0 30 52 84 118 154 222 240 262 280 348 384 418 450 472 502	1242982531772