Prime p₀= 797133051003635789 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 16 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 78 80 120 122
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: 122
Found by: [SG-2W]Kurzer
db: batch=73, k=10, 2 40 2 16 2

SPT(16)	797132089064410261	0 10 12 28 70 78 88 112 138 162 172 180 222 238 240 250	-961939225528
TPT(14)	797132259405839099	0 2 12 14 42 44 72 74 78 80 138 140 150 152	-791597796690
STPT(10)	797132397411584189	0 2 42 44 90 92 138 140 180 182	-653592051600
SPT(16)	797132630946109691	0 30 72 132 158 182 198 212 288 302 318 342 368 428 470 500	-420057526098
TPT(14)	797132720529901211	0 2 30 32 78 80 96 98 108 110 198 200 210 212	-330473734578
TPT(14)	797132790076948847	0 2 12 14 30 32 84 86 240 242 354 356 384 386	-260926686942
STPT(10)	797133056022758027	0 2 24 26 42 44 60 62 84 86	5019122238
STPT(10)	797133943954214897	0 2 30 32 60 62 90 92 120 122	892950579108
SPT(16)	797133982299207737	0 20 44 84 134 192 204 224 240 260 272 330 380 420 444 464	931295571948
SPT(16)	797134292033997859	0 12 42 60 100 118 142 172 210 240 264 282 322 340 370 382	1241030362070
SPT(16)	797134658463884093	0 36 38 44 66 78 108 114 140 146 176 188 210 216 218 254	1607460248304