Prime p₀= 2301021172479254567 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: MarkRBright
db: batch=81, k=10, 2 22 2 16 2

SPT(16)	2301020148206786711	0 8 20 42 92 102 146 150 158 162 206 216 266 288 300 308	-1024272467856
SPT(16)	2301020277832655381	0 8 62 66 80 92 168 216 242 290 366 378 392 396 450 458	-894646599186
TPT(14)	2301020339924329757	0 2 24 26 54 56 192 194 222 224 264 266 282 284	-832554924810
STPT(10)	2301020557668383597	0 2 54 56 72 74 90 92 144 146	-614810870970
SPT(16)	2301020562676776013	0 16 28 54 120 184 190 234 250 294 300 364 430 456 468 484	-609802478554
SPT(16)	2301020784700642429	0 18 88 94 112 162 174 190 192 208 220 270 288 294 364 382	-387778612138
SPT(16)	2301021317548877141	0 18 56 72 116 122 126 150 158 182 186 192 236 252 290 308	145069622574
STPT(10)	2301021413764538219	0 2 18 20 30 32 42 44 60 62	241285283652
STPT(10)	2301021737734108967	0 2 30 32 42 44 54 56 84 86	565254854400
STPT(10)	2301022487658510401	0 2 30 32 60 62 90 92 120 122	1315179255834
STPT(10)	2301023425539183617	0 2 24 26 42 44 60 62 84 86	2253059929050