Prime p₀= 1508004804362716001 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 58 2 106 2 106 2 58 2 (?)
a_n: 0 2 60 62 168 170 276 278 336 338
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: 338
Found by: crashtech
db: batch=78, k=10, 2 58 2 106 2

SPT(16)	1508004019848793751	0 32 50 56 162 180 182 218 270 306 308 326 432 438 456 488	-784513922250
SPT(16)	1508004338608326469	0 4 30 60 70 88 124 130 138 144 180 198 208 238 264 268	-465754389532
SPT(16)	1508004567078611027	0 62 66 86 200 270 324 342 434 452 506 576 690 710 714 776	-237284104974
STPT(10)	1508004679047436649	0 2 48 50 60 62 72 74 120 122	-125315279352
STPT(10)	1508004788319975521	0 2 36 38 78 80 120 122 156 158	-16042740480
SPT(16)	1508004788936393617	0 30 34 70 90 100 150 154 156 160 210 220 240 276 280 310	-15426322384
SPT(16)	1508005099084575131	0 6 36 50 78 98 120 192 206 278 300 320 348 362 392 398	294721859130
STPT(10)	1508005199457872117	0 2 30 32 60 62 90 92 120 122	395095156116
SPT(20)	1508005358108103817	0 6 40 42 54 76 120 132 154 190 216 252 274 286 330 352 364 366 400 406	553745387816
SPT(16)	1508005422583901291	0 26 32 50 56 92 110 128 150 168 186 222 228 246 252 278	618221185290
STPT(10)	1508005434788976047	0 2 12 14 42 44 72 74 84 86	630426260046