Prime p₀= 3571435012988501801 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: [SG]KidDoesCrunch
db: batch=84, k=10, 2 4 2 10 2

TPT(14)	3571432870243237499	0 2 42 44 78 80 108 110 168 170 258 260 300 302	-2142745264302
SPT(16)	3571432980747310829	0 2 8 24 38 120 128 138 164 174 182 264 278 294 300 302	-2032241190972
SPT(16)	3571433814296546837	0 42 114 116 134 162 182 192 224 234 254 282 300 302 374 416	-1198691954964
SPT(16)	3571434003572605759	0 40 58 78 102 184 238 250 252 264 318 400 424 444 462 502	-1009415896042
STPT(10)	3571434853375560011	0 2 36 38 78 80 120 122 156 158	-159612941790
TPT(14)	3571434990891945239	0 2 18 20 60 62 72 74 150 152 168 170 192 194	-22096556562
STPT(10)	3571435286837577317	0 2 54 56 72 74 90 92 144 146	273849075516
SPT(16)	3571435333349072419	0 10 28 52 60 88 94 198 214 318 324 352 360 384 402 412	320360570618
STPT(10)	3571435424681680481	0 2 30 32 78 80 126 128 156 158	411693178680
SPT(16)	3571435749436960511	0 2 8 66 68 110 126 138 140 152 168 210 212 270 276 278	736448458710
SPT(16)	3571436030084363593	0 10 34 54 64 78 94 168 256 330 346 360 370 390 414 424	1017095861792