Prime p₀= 3679924637616254717 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

STPT(10)	3679923057926812517	0 2 60 62 72 74 84 86 144 146	-1579689442200
SPT(16)	3679923213083548183	0 96 148 154 156 210 258 280 294 316 364 418 420 426 478 574	-1424532706534
STPT(10)	3679923301131862451	0 2 6 8 18 20 30 32 36 38	-1336484392266
STPT(10)	3679923419300167181	0 2 6 8 18 20 30 32 36 38	-1218316087536
SPT(16)	3679923994705209863	0 8 30 44 68 86 108 140 204 236 258 276 300 314 336 344	-642911044854
SPT(13)	3679924313694048481	0 12 18 42 48 78 90 102 132 138 162 168 180	-323922206236
STPT(10)	3679924773595962251	0 2 6 8 48 50 90 92 96 98	135979707534
SPT(16)	3679925236327475671	0 42 46 106 112 172 180 250 372 442 450 510 516 576 580 622	598711220954
SPT(22)	3679925707617846839	0 8 14 50 54 78 80 92 98 102 104 138 140 144 150 162 164 188 192 228 234 242	1070001592122
STPT(10)	3679926577199592677	0 2 42 44 72 74 102 104 144 146	1939583337960
STPT(10)	3679926610806797621	0 2 6 8 48 50 90 92 96 98	1973190542904