Prime p₀= 772809618961105931 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: scrap
db: batch=73, k=10, 2 4 2 10 2

SPT(16)	772808822768613497	0 6 14 32 44 54 230 236 270 276 452 462 474 492 500 506	-796192492434
STPT(10)	772808900426253149	0 2 18 20 30 32 42 44 60 62	-718534852782
STPT(10)	772809170841108197	0 2 30 32 42 44 54 56 84 86	-448119997734
SPT(16)	772809221957893291	0 12 70 112 118 156 178 196 222 240 262 300 306 348 406 418	-397003212640
SPT(16)	772809455942796539	0 12 42 68 72 80 122 150 182 210 252 260 264 290 320 332	-163018309392
SPT(16)	772809485774959667	0 6 12 26 110 140 180 210 212 242 282 312 396 410 416 422	-133186146264
SPT(16)	772809740037704507	0 6 12 56 62 80 102 150 266 314 336 354 360 404 410 416	121076598576
SPT(16)	772810518291020747	0 14 30 42 62 104 132 146 180 194 222 264 284 296 312 326	899329914816
SPT(16)	772810560447930649	0 10 12 30 42 52 54 88 204 238 240 250 262 280 282 292	941486824718
STPT(12)	772810694478417599	0 2 30 32 42 44 90 92 102 104 132 134	1075517311668
STPT(10)	772811362018617707	0 2 30 32 60 62 90 92 120 122	1743057511776