Prime p₀= 1267439120048750837 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: Megacruncher
db: batch=77, k=10, 2 22 2 16 2

TPT(14)	1267438434842449391	0 2 18 20 90 92 168 170 186 188 228 230 300 302	-685206301446
SPT(16)	1267438442058325631	0 6 20 30 56 98 108 156 182 230 240 282 308 318 332 338	-677990425206
SPT(16)	1267438470138363113	0 48 54 68 78 96 108 140 174 206 218 236 246 260 266 314	-649910387724
SPT(16)	1267438471211712479	0 44 50 114 140 168 170 210 362 402 404 432 458 522 528 572	-648837038358
STPT(10)	1267439017317951617	0 2 12 14 42 44 72 74 84 86	-102730799220
SPT(16)	1267439044665944639	0 2 42 80 108 140 150 164 198 212 222 254 282 320 360 362	-75382806198
TPT(14)	1267439274003205139	0 2 48 50 72 74 90 92 102 104 180 182 198 200	153954454302
SPT(16)	1267439412224472001	0 6 36 40 138 168 246 280 306 340 418 448 546 550 580 586	292175721164
STPT(10)	1267439604845047631	0 2 6 8 48 50 90 92 96 98	484796296794
STPT(10)	1267439672700980921	0 2 6 8 18 20 30 32 36 38	552652230084
SPT(16)	1267440055689246563	0 14 20 38 80 104 108 116 168 176 180 204 246 264 270 284	935640495726