Prime p₀= 3717732687855751151 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 106 2 28 2 28 2 106 2 (?)
a_n: 0 2 108 110 138 140 168 170 276 278
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: 278
Found by: Sphynx
db: batch=84, k=10, 2 106 2 28 2

SPT(16)	3717732064606390841	0 26 30 48 66 72 86 110 168 192 206 212 230 248 252 278	-623249360310
SPT(16)	3717732084132515599	0 22 40 132 148 168 192 204 208 220 244 264 280 372 390 412	-603723235552
SPT(16)	3717732204704445833	0 24 44 120 146 170 188 246 308 366 384 408 434 510 530 554	-483151305318
STPT(10)	3717732280051856777	0 2 12 14 42 44 72 74 84 86	-407803894374
SPT(16)	3717732307696910599	0 12 78 90 144 154 160 172 210 222 228 238 292 304 370 382	-380158840552
SPT(16)	3717732368051779967	0 14 32 36 54 96 102 110 126 134 140 182 200 204 222 236	-319803971184
SPT(16)	3717732711996925429	0 34 70 78 114 118 150 162 190 202 234 238 274 282 318 352	24141174278
STPT(10)	3717732775714440149	0 2 42 44 60 62 78 80 120 122	87858688998
STPT(10)	3717733058865523667	0 2 30 32 72 74 114 116 144 146	371009772516
STPT(10)	3717733080890382857	0 2 30 32 120 122 210 212 240 242	393034631706
STPT(10)	3717733392401626571	0 2 78 80 138 140 198 200 276 278	704545875420