Prime p₀= 4044852957745909427 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: Alnitak2019
db: batch=84, k=10, 2 22 2 16 2

STPT(10)	4044852175554368441	0 2 6 8 48 50 90 92 96 98	-782191540986
SPT(16)	4044852382237422893	0 68 74 96 114 134 230 236 288 294 390 410 428 450 456 524	-575508486534
SPT(16)	4044852419759199619	0 28 30 58 84 124 142 154 168 180 198 238 264 292 294 322	-537986709808
TPT(14)	4044852538576188791	0 2 6 8 48 50 60 62 126 128 138 140 156 158	-419169720636
STPT(10)	4044852596497578989	0 2 12 14 30 32 48 50 60 62	-361248330438
STPT(10)	4044852602588668691	0 2 6 8 18 20 30 32 36 38	-355157240736
SPT(16)	4044853216072938991	0 18 30 36 42 52 66 100 108 142 156 166 172 178 190 208	258327029564
STPT(10)	4044853347088173671	0 2 6 8 18 20 30 32 36 38	389342264244
TPT(14)	4044853549602060749	0 2 138 140 180 182 222 224 288 290 378 380 420 422	591856151322
SPT(16)	4044853596244472021	0 2 62 66 132 138 140 170 258 288 290 296 362 366 426 428	638498562594
SPT(16)	4044854005514085451	0 6 10 58 88 100 108 160 168 220 228 240 270 318 322 328	1047768176024