Prime p₀= 4410910853357878937 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: [SG]KidDoesCrunch
db: batch=85, k=10, 2 10 2 28 2

TPT(14)	4410909606076787621	0 2 36 38 78 80 150 152 168 170 300 302 318 320	-1247281091316
SPT(16)	4410909615744006229	0 4 12 22 52 100 108 144 148 184 192 240 270 280 288 292	-1237613872708
STPT(10)	4410910179713383271	0 2 30 32 78 80 126 128 156 158	-673644495666
STPT(10)	4410910201065484811	0 2 30 32 60 62 90 92 120 122	-652292394126
SPT(16)	4410910568523024887	0 2 24 44 54 66 80 126 170 216 230 242 252 272 294 296	-284834854050
SPT(22)	4410910708565406883	0 34 48 88 126 144 204 210 216 244 264 370 390 418 424 430 490 508 546 586 600 634	-144792472054
STPT(10)	4410910967191460759	0 2 18 20 30 32 42 44 60 62	113833581822
SPT(16)	4410911279461147387	0 34 42 54 90 114 210 220 264 274 370 394 430 442 450 484	426103268450
SPT(16)	4410911486782085567	0 20 32 36 60 90 144 170 216 242 296 326 350 354 366 386	633424206630
SPT(16)	4410911943189961327	0 4 42 60 70 76 94 112 114 132 150 156 166 184 222 226	1089832082390
STPT(10)	4410912026028480197	0 2 30 32 42 44 54 56 84 86	1172670601260