Prime p₀= 2317500347355672077 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)	2317498280141118287	0 6 12 14 20 42 56 66 80 90 104 126 132 134 140 146	-2067214553790
STPT(10)	2317498935316956497	0 2 30 32 42 44 54 56 84 86	-1412038715580
SPT(16)	2317499363593572527	0 42 96 116 146 162 176 200 252 276 290 306 336 356 410 452	-983762099550
SPT(16)	2317499643054406583	0 38 56 78 90 108 216 240 266 290 398 416 428 450 468 506	-704301265494
STPT(10)	2317499997193666457	0 2 30 32 42 44 54 56 84 86	-350162005620
TPT(14)	2317500289688603267	0 2 54 56 84 86 132 134 162 164 174 176 210 212	-57667068810
SPT(16)	2317501015296059311	0 46 82 108 130 132 162 186 322 346 376 378 400 426 462 508	667940387234
SPT(16)	2317501183380234097	0 82 94 96 100 112 114 156 250 292 294 306 310 312 324 406	836024562020
SPT(16)	2317501240176198229	0 30 52 84 118 154 222 240 262 280 348 384 418 450 472 502	892820526152
STPT(10)	2317501330258850579	0 2 18 20 30 32 42 44 60 62	982903178502
SPT(16)	2317501379747193517	0 22 30 66 100 106 124 150 166 192 210 216 250 286 294 316	1032391521440