Prime p₀= 1298022422880025991 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 36 38 78 80 120 122 156 158
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: 158
Found by: Cruncher Pete
db: batch=77, k=10, 2 34 2 40 2

SPT(16)	1298021075617789297	0 34 42 46 64 76 90 120 136 166 180 192 210 214 222 256	-1347262236694
SPT(16)	1298021266511812093	0 28 30 118 168 184 220 226 228 234 270 286 336 424 426 454	-1156368213898
STPT(10)	1298021311785723911	0 2 126 128 138 140 150 152 276 278	-1111094302080
STPT(10)	1298021962669148411	0 2 30 32 60 62 90 92 120 122	-460210877580
TPT(14)	1298022015189593717	0 2 60 62 72 74 84 86 114 116 204 206 240 242	-407690432274
SPT(16)	1298022399318656881	0 16 22 36 46 60 78 90 268 280 298 312 322 336 342 358	-23561369110
STPT(10)	1298022569337334661	0 2 6 8 18 20 30 32 36 38	146457308670
STPT(10)	1298022831190912031	0 2 6 8 18 20 30 32 36 38	408310886040
SPT(16)	1298022838945460011	0 82 112 118 160 192 196 202 216 222 226 258 300 306 336 418	416065434020
STPT(10)	1298022969138394529	0 2 18 20 30 32 42 44 60 62	546258368538
SPT(16)	1298023218649886761	0 6 22 42 76 96 112 120 172 180 196 216 250 270 286 292	795769860770