Prime p₀= 4276904082288275507 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: Autofuzzy
db: batch=85, k=10, 2 22 2 16 2

STPT(10)	4276901486364923957	0 2 30 32 72 74 114 116 144 146	-2595923351550
STPT(10)	4276902545592799037	0 2 24 26 42 44 60 62 84 86	-1536695476470
SPT(20)	4276902961160113079	0 12 38 50 78 102 110 138 152 158 252 258 272 300 308 332 360 372 398 410	-1121128162428
TPT(14)	4276903529108988989	0 2 30 32 78 80 168 170 180 182 198 200 222 224	-553179286518
SPT(16)	4276903720358567099	0 54 102 104 152 174 180 200 204 224 230 252 300 302 350 404	-361929708408
SPT(16)	4276903806984955441	0 18 28 72 78 88 96 120 148 172 180 190 196 240 250 268	-275303320066
STPT(10)	4276904425824510281	0 2 6 8 48 50 90 92 96 98	343536234774
STPT(10)	4276904616315309239	0 2 48 50 60 62 72 74 120 122	534027033732
SPT(16)	4276904858089605901	0 22 40 48 108 118 120 150 178 208 210 220 280 288 306 328	775801330394
SPT(16)	4276905210435484111	0 30 36 78 132 192 198 238 240 280 286 346 400 442 448 478	1128147208604
STPT(10)	4276905581169680351	0 2 6 8 48 50 90 92 96 98	1498881404844