Prime p₀= 1299478285163242157 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: Cruncher Pete
db: batch=77, k=10, 2 28 2 10 2

SPT(16)	1299477454943829769	0 90 114 132 138 180 192 222 280 310 322 364 370 388 412 502	-830219412388
STPT(10)	1299477960078751931	0 2 30 32 78 80 126 128 156 158	-325084490226
SPT(16)	1299477975711880609	0 10 28 30 52 58 64 82 210 228 234 240 262 264 282 292	-309451361548
SPT(16)	1299478054278286903	0 4 30 100 126 138 186 196 198 208 256 268 294 364 390 394	-230884955254
STPT(10)	1299478092174644279	0 2 18 20 60 62 102 104 120 122	-192988597878
STPT(10)	1299478151927327891	0 2 36 38 78 80 120 122 156 158	-133235914266
STPT(10)	1299478942226759051	0 2 6 8 18 20 30 32 36 38	657063516894
STPT(10)	1299478962696167777	0 2 30 32 42 44 54 56 84 86	677532925620
SPT(16)	1299479183126482507	0 4 10 100 114 120 142 144 160 162 184 190 204 294 300 304	897963240350
STPT(10)	1299479500493529527	0 2 30 32 42 44 54 56 84 86	1215330287370
SPT(16)	1299479527039260647	0 12 20 26 72 86 120 146 156 182 216 230 276 282 290 302	1241876018490