Prime p₀= 976876596726375647 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: Spectrum
db: batch=76, k=10, 2 28 2 10 2

STPT(10)	976875355696921529	0 2 30 32 60 62 90 92 120 122	-1241029454118
TPT(14)	976875750375842789	0 2 138 140 162 164 168 170 192 194 222 224 258 260	-846350532858
SPT(16)	976875894225411781	0 40 46 52 60 66 76 82 96 102 112 118 126 132 138 178	-702500963866
STPT(10)	976876062941153621	0 2 36 38 78 80 120 122 156 158	-533785222026
SPT(16)	976876324903155163	0 6 58 100 180 196 244 264 310 330 378 394 474 516 568 574	-271823220484
STPT(10)	976876474607170901	0 2 30 32 78 80 126 128 156 158	-122119204746
SPT(16)	976877453431666009	0 34 72 90 132 144 150 172 240 262 268 280 322 340 378 412	856705290362
SPT(16)	976877494175977573	0 4 28 48 54 58 76 106 138 168 186 190 196 216 240 244	897449601926
SPT(16)	976877555673084391	0 16 78 96 100 118 120 198 208 286 288 306 310 328 390 406	958946708744
SPT(16)	976877605781287633	0 64 66 76 78 120 168 180 304 316 364 406 408 418 420 484	1009054911986
STPT(10)	976877893713381659	0 2 18 20 30 32 42 44 60 62	1296987006012