Prime p₀= 2356562567858004629 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 16 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 48 50 60 62
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: 62
Found by: Landjunge
db: batch=81, k=10, 2 10 2 16 2

TPT(14)	2356561747791079529	0 2 30 32 42 44 138 140 180 182 198 200 240 242	-820066925100
SPT(16)	2356562019213416747	0 24 36 122 132 140 194 266 270 342 396 404 414 500 512 536	-548644587882
SPT(16)	2356562172641377979	0 18 32 68 78 80 110 144 158 192 222 224 234 270 284 302	-395216626650
SPT(16)	2356562173931716981	0 6 28 60 126 130 132 168 220 256 258 262 328 360 382 388	-393926287648
STPT(10)	2356562250739873901	0 2 6 8 48 50 90 92 96 98	-317118130728
SPT(16)	2356562354026247467	0 24 34 46 66 70 84 90 106 112 126 130 150 162 172 196	-213831757162
SPT(16)	2356562615191176547	0 64 70 124 126 130 180 210 226 256 306 310 312 366 372 436	47333171918
SPT(16)	2356562740168291271	0 8 12 18 42 56 80 110 168 198 222 236 260 266 270 278	172310286642
TPT(16)	2356563615895358237	0 2 12 14 30 32 60 62 84 86 210 212 294 296 522 524	1048037353608
STPT(10)	2356564247031247397	0 2 60 62 72 74 84 86 144 146	1679173242768
SPT(16)	2356564790716482881	0 2 12 30 86 110 176 192 236 252 318 342 398 416 426 428	2222858478252