Prime p₀= 2123534316337809017 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 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: Chooka
db: batch=80, k=10, 2 22 2 16 2

STPT(10)	2123533213462016141	0 2 30 32 78 80 126 128 156 158	-1102875792876
STPT(10)	2123533610517658991	0 2 36 38 78 80 120 122 156 158	-705820150026
SPT(16)	2123533616131398799	0 82 124 130 132 142 180 184 198 202 240 250 252 258 300 382	-700206410218
SPT(16)	2123534065123820413	0 28 54 58 64 70 100 148 186 234 264 270 276 280 306 334	-251213988604
SPT(16)	2123534070932485187	0 12 30 32 86 96 104 140 216 252 260 270 324 326 344 356	-245405323830
SPT(16)	2123534309655792151	0 10 28 30 42 70 72 108 160 196 198 226 238 240 258 268	-6682016866
STPT(10)	2123534498104490267	0 2 24 26 42 44 60 62 84 86	181766681250
SPT(16)	2123534964465440293	0 48 76 118 120 138 186 264 280 358 406 424 426 468 496 544	648127631276
SPT(16)	2123535109414142989	0 22 52 90 94 130 160 168 214 222 252 288 292 330 360 382	793076333972
STPT(10)	2123535185148579029	0 2 42 44 60 62 78 80 120 122	868810770012
SPT(16)	2123535448364644849	0 22 42 54 64 120 168 178 234 244 292 348 358 370 390 412	1132026835832