Prime p₀= 1241051682806399369 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 76 2 76 2 10 2 (?)
a_n: 0 2 12 14 90 92 168 170 180 182
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: 182
Found by: Cruncher Pete
db: batch=77, k=10, 2 10 2 76 2

SPT(16)	1241050735140236429	0 14 44 84 132 164 170 188 234 252 258 290 338 378 408 422	-947666162940
TPT(14)	1241051107391652209	0 2 42 44 72 74 90 92 132 134 162 164 168 170	-575414747160
SPT(16)	1241051146700476333	0 6 34 60 96 120 180 210 334 364 424 448 484 510 538 544	-536105923036
STPT(10)	1241051357337597077	0 2 30 32 42 44 54 56 84 86	-325468802292
SPT(16)	1241051452025811001	0 88 118 130 142 162 168 192 196 220 226 246 258 270 300 388	-230780588368
SPT(16)	1241051610709565267	0 26 116 132 152 156 162 170 186 194 200 204 224 240 330 356	-72096834102
STPT(10)	1241051712151648751	0 2 6 8 48 50 90 92 96 98	29345249382
SPT(16)	1241051888575908217	0 30 34 70 76 100 112 130 156 174 186 210 216 252 256 286	205769508848
SPT(16)	1241052333988479989	0 18 42 48 84 98 120 132 140 152 174 188 224 230 254 272	651182080620
STPT(10)	1241052451509630581	0 2 6 8 48 50 90 92 96 98	768703231212
STPT(10)	1241052765565467269	0 2 18 20 30 32 42 44 60 62	1082759067900