Prime p₀= 1231578649631443037 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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 10 2 28 2

SPT(16)	1231577108471917751	0 12 42 66 146 176 180 222 230 272 276 306 386 410 440 452	-1541159525286
SPT(16)	1231577505830674333	0 16 24 66 78 84 88 100 114 126 130 136 148 190 198 214	-1143800768704
SPT(16)	1231577659369860499	0 12 42 82 112 124 142 168 184 210 228 240 270 310 340 352	-990261582538
SPT(16)	1231577936642790673	0 30 34 58 66 70 84 88 96 100 114 118 126 150 154 184	-712988652364
STPT(10)	1231578518776941659	0 2 42 44 60 62 78 80 120 122	-130854501378
SPT(16)	1231578588327038513	0 48 56 78 84 146 158 206 228 276 288 350 356 378 386 434	-61304404524
STPT(10)	1231578860217247427	0 2 30 32 42 44 54 56 84 86	210585804390
SPT(16)	1231578883853752249	0 18 70 100 144 154 160 168 214 222 228 238 282 312 364 382	234222309212
TPT(14)	1231579066359592187	0 2 12 14 30 32 72 74 210 212 222 224 282 284	416728149150
STPT(10)	1231579096235704817	0 2 30 32 42 44 54 56 84 86	446604261780
SPT(16)	1231579164918264469	0 42 60 82 88 102 108 114 238 244 250 264 270 292 310 352	515286821432