Prime p₀= 1267854128986538537 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 88 2 88 2 40 2 (?)
a_n: 0 2 42 44 132 134 222 224 264 266
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: 266
Found by: Megacruncher
db: batch=77, k=10, 2 40 2 88 2

TPT(14)	1267853209195723877	0 2 24 26 150 152 210 212 264 266 270 272 282 284	-919790814660
STPT(10)	1267853343637379669	0 2 78 80 120 122 162 164 240 242	-785349158868
SPT(16)	1267853744919128119	0 34 42 58 78 82 124 142 180 198 240 244 264 280 288 322	-384067410418
SPT(16)	1267853779374911297	0 2 24 30 62 74 132 150 164 182 240 252 284 290 312 314	-349611627240
SPT(16)	1267853930098956113	0 20 50 56 86 96 104 114 200 210 218 228 258 264 294 314	-198887582424
SPT(16)	1267854106759698947	0 32 56 66 74 126 132 144 152 164 170 222 230 240 264 296	-22226839590
SPT(16)	1267854205921079879	0 20 42 84 90 104 114 170 174 230 240 254 260 302 324 344	76934541342
STPT(10)	1267854459152906897	0 2 24 26 42 44 60 62 84 86	330166368360
STPT(10)	1267854802005963539	0 2 18 20 30 32 42 44 60 62	673019425002
STPT(10)	1267854908915319971	0 2 36 38 78 80 120 122 156 158	779928781434
TPT(14)	1267854992013154229	0 2 42 44 102 104 180 182 192 194 222 224 240 242	863026615692