Prime p₀= 2579569109884476557 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: JayPi
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2579568620081795327	0 12 30 42 56 66 90 102 110 122 146 156 170 182 200 212	-489802681230
SPT(16)	2579568652927174199	0 32 42 62 92 158 198 212 258 272 312 378 408 428 438 470	-456957302358
SPT(16)	2579568888945520193	0 18 30 98 120 168 194 200 204 210 236 284 306 374 386 404	-220938956364
TPT(14)	2579568899314170809	0 2 78 80 90 92 108 110 132 134 138 140 210 212	-210570305748
SPT(16)	2579568939145105249	0 24 30 82 124 172 174 184 210 220 222 270 312 364 370 394	-170739371308
TPT(14)	2579568977157776621	0 2 6 8 78 80 90 92 108 110 138 140 216 218	-132726699936
STPT(10)	2579569425213752747	0 2 12 14 42 44 72 74 84 86	315329276190
SPT(16)	2579569614587713309	0 4 22 34 58 78 90 94 168 172 184 204 228 240 258 262	504703236752
STPT(10)	2579569926691529669	0 2 42 44 60 62 78 80 120 122	816807053112
STPT(10)	2579570359651614149	0 2 42 44 60 62 78 80 120 122	1249767137592
SPT(16)	2579570390405006891	0 60 62 116 126 162 168 176 222 230 236 272 282 336 338 398	1280520530334