Prime p₀= 2068564442065046087 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: Cruncher Pete
db: batch=80, k=10, 2 28 2 10 2

STPT(10)	2068563663048532421	0 2 36 38 78 80 120 122 156 158	-779016513666
SPT(16)	2068563705274000289	0 20 42 54 62 84 98 104 138 144 158 180 188 200 222 242	-736791045798
STPT(10)	2068563781889540237	0 2 30 32 42 44 54 56 84 86	-660175505850
SPT(16)	2068563821998451773	0 4 10 64 66 114 118 238 276 396 400 448 450 504 510 514	-620066594314
STPT(10)	2068564016972401769	0 2 42 44 60 62 78 80 120 122	-425092644318
SPT(16)	2068564314854598637	0 6 24 40 70 90 124 150 160 186 220 240 270 286 304 310	-127210447450
SPT(16)	2068564467211124587	0 6 24 130 174 214 256 300 316 360 402 442 486 592 610 616	25146078500
SPT(16)	2068564533106865141	0 6 78 90 152 162 206 210 398 402 446 456 518 530 602 608	91041819054
SPT(16)	2068564630520707349	0 30 60 84 90 114 174 254 258 338 398 422 428 452 482 512	188455661262
STPT(10)	2068564729064001401	0 2 30 32 78 80 126 128 156 158	286998955314
STPT(10)	2068564773127458797	0 2 90 92 102 104 114 116 204 206	331062412710