Prime p₀= 1268558732286524867 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

STPT(10)	1268557768314143297	0 2 12 14 42 44 72 74 84 86	-963972381570
SPT(16)	1268557773992021687	0 6 30 44 62 72 122 192 254 324 374 384 402 416 440 446	-958294503180
SPT(16)	1268557903399943509	0 12 22 52 108 162 204 220 222 238 280 334 390 420 430 442	-828886581358
SPT(16)	1268557929993265271	0 38 68 90 96 98 192 198 230 236 330 332 338 360 390 428	-802293259596
STPT(10)	1268558123908478237	0 2 42 44 102 104 162 164 204 206	-608378046630
TPT(14)	1268558535871890749	0 2 78 80 180 182 222 224 330 332 360 362 498 500	-196414634118
STPT(10)	1268558828807797727	0 2 54 56 72 74 90 92 144 146	96521272860
SPT(16)	1268559067581830723	0 14 18 30 98 108 128 156 158 186 206 216 284 296 300 314	335295305856
SPT(16)	1268559369959471741	0 26 48 50 78 132 170 182 216 228 266 320 348 350 372 398	637672946874
SPT(16)	1268559464605840273	0 28 48 88 130 138 150 166 180 196 208 216 258 298 318 346	732319315406
SPT(16)	1268559473382965419	0 12 18 42 90 118 120 148 192 220 222 250 298 322 328 340	741096440552