Prime p₀= 1123791625363761857 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: crashtech
db: batch=76, k=10, 2 22 2 16 2

STPT(10)	1123790673979167167	0 2 30 32 42 44 54 56 84 86	-951384594690
STPT(10)	1123790775007698767	0 2 30 32 72 74 114 116 144 146	-850356063090
STPT(10)	1123790818216455197	0 2 54 56 72 74 90 92 144 146	-807147306660
STPT(10)	1123791164666884451	0 2 6 8 108 110 210 212 216 218	-460696877406
SPT(16)	1123791228257350111	0 18 28 60 70 72 118 142 156 180 226 228 238 270 280 298	-397106411746
SPT(13)	1123791319862374643	0 30 126 156 174 216 240 264 306 324 354 450 480	-305501387214
STPT(10)	1123791921082662437	0 2 60 62 72 74 84 86 144 146	295718900580
SPT(16)	1123791982584014867	0 12 60 110 114 132 140 146 180 186 194 212 216 266 314 326	357220253010
SPT(16)	1123792103987302283	0 8 18 20 24 30 66 78 86 98 134 140 144 146 156 164	478623540426
SPT(16)	1123792583887842403	0 30 34 54 58 64 78 96 178 196 210 216 220 240 244 274	958524080546
SPT(20)	1123792596876253181	0 20 26 86 120 126 132 146 152 168 260 276 282 296 302 308 342 402 408 428	971512491324