Prime p₀= 3565551370055329397 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: [SG]KidDoesCrunch
db: batch=84, k=10, 2 28 2 10 2

TPT(14)	3565548236343050777	0 2 210 212 240 242 264 266 282 284 330 332 372 374	-3133712278620
TPT(14)	3565549567947253979	0 2 120 122 138 140 180 182 198 200 222 224 240 242	-1802108075418
SPT(16)	3565550084441904719	0 14 24 72 128 132 150 200 222 272 290 294 350 398 408 422	-1285613424678
STPT(10)	3565550239289563541	0 2 30 32 78 80 126 128 156 158	-1130765765856
SPT(16)	3565551000643357811	0 12 26 116 150 158 210 236 282 308 360 368 402 492 506 518	-369411971586
SPT(16)	3565551171268725293	0 6 26 54 68 116 128 156 158 186 198 246 260 288 308 314	-198786604104
SPT(16)	3565551599083821947	0 12 42 62 66 80 90 174 182 266 276 290 294 314 344 356	229028492550
TPT(14)	3565551658266092951	0 2 30 32 126 128 150 152 210 212 276 278 288 290	288210763554
TPT(14)	3565551684219451349	0 2 12 14 90 92 150 152 222 224 252 254 372 374	314164121952
SPT(16)	3565552429821026069	0 24 50 68 78 84 90 122 150 182 188 194 204 222 248 272	1059765696672
SPT(16)	3565553280985297517	0 2 12 14 102 104 144 146 180 182 222 224 312 314 324 326	1910929968120