Prime p₀= 3679927475856896321 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 120 122 156 158
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: 158
Found by: [SG]KidDoesCrunch
db: batch=84, k=10, 2 34 2 40 2

SPT(16)	3679925236327475671	0 42 46 106 112 172 180 250 372 442 450 510 516 576 580 622	-2239529420650
SPT(22)	3679925707617846839	0 8 14 50 54 78 80 92 98 102 104 138 140 144 150 162 164 188 192 228 234 242	-1768239049482
STPT(10)	3679926577199592677	0 2 42 44 72 74 102 104 144 146	-898657303644
STPT(10)	3679926610806797621	0 2 6 8 48 50 90 92 96 98	-865050098700
STPT(10)	3679926798898771229	0 2 48 50 90 92 132 134 180 182	-676958125092
SPT(16)	3679927162537506971	0 30 98 126 128 132 146 206 282 342 356 360 362 390 458 488	-313319389350
SPT(16)	3679927644287944789	0 24 48 64 90 94 108 148 180 220 234 238 264 280 304 328	168431048468
SPT(16)	3679928170780086209	0 14 98 110 134 144 168 180 182 194 218 228 252 264 348 362	694923189888
STPT(10)	3679928489846287997	0 2 84 86 132 134 180 182 264 266	1013989391676
SPT(16)	3679929470957467187	0 12 26 42 50 92 102 120 206 224 234 276 284 300 314 326	1995100570866
STPT(10)	3679929714710233637	0 2 72 74 102 104 132 134 204 206	2238853337316