Prime p₀= 812570578415032637 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 58 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 132 134 144 146
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: 146
Found by: [SG]FX
db: batch=73, k=10, 2 10 2 58 2

SPT(16)	812569261148551799	0 12 62 72 84 90 132 144 170 182 224 230 242 252 302 314	-1317266480838
STPT(10)	812569425285148589	0 2 42 44 60 62 78 80 120 122	-1153129884048
SPT(16)	812569473568999171	0 6 22 28 58 70 72 90 148 166 168 180 210 216 232 238	-1104846033466
SPT(18)	812569853241649621	0 6 28 30 40 42 60 82 118 150 186 208 226 228 238 240 262 268	-725173383016
STPT(10)	812569921253298389	0 2 18 20 30 32 42 44 60 62	-657161734248
STPT(10)	812570540117705261	0 2 6 8 48 50 90 92 96 98	-38297327376
SPT(16)	812571489206015897	0 26 30 42 56 120 222 224 282 284 386 450 464 476 480 506	910790983260
STPT(10)	812571807273835559	0 2 18 20 30 32 42 44 60 62	1228858802922
STPT(10)	812571937151220941	0 2 36 38 78 80 120 122 156 158	1358736188304
SPT(16)	812572073377350883	0 18 28 48 70 88 148 150 154 156 216 234 256 276 286 304	1494962318246
STPT(10)	812572212972968387	0 2 30 32 60 62 90 92 120 122	1634557935750