Prime p₀= 768065348051204657 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: GLeeM
db: batch=73, k=10, 2 22 2 16 2

STPT(10)	768063717569939699	0 2 18 20 30 32 42 44 60 62	-1630481264958
SPT(16)	768064271969198177	0 30 72 84 114 140 182 212 234 264 306 332 362 374 416 446	-1076082006480
SPT(16)	768064813436313551	0 42 48 60 68 72 78 98 132 152 158 162 170 182 188 230	-534614891106
SPT(16)	768064902897018383	0 20 30 44 86 126 174 200 324 350 398 438 480 494 504 524	-445154186274
SPT(16)	768065172764224163	0 6 36 38 78 98 110 156 188 234 246 266 306 308 338 344	-175286980494
SPT(16)	768065301539023921	0 16 60 72 108 196 208 222 226 240 252 340 376 388 432 448	-46512180736
STPT(12)	768065394126620921	0 2 36 38 48 50 78 80 90 92 126 128	46075416264
STPT(10)	768065408547044519	0 2 18 20 30 32 42 44 60 62	60495839862
STPT(10)	768065447042260361	0 2 36 38 78 80 120 122 156 158	98991055704
STPT(10)	768065454059906381	0 2 36 38 78 80 120 122 156 158	106008701724
SPT(16)	768065920017863227	0 4 10 34 40 54 66 94 126 154 166 180 186 210 216 220	571966658570