Prime p₀= 4305790737878246117 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 58 2 58 2 10 2 (?)
a_n: 0 2 12 14 72 74 132 134 144 146
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: 146
Found by: Chooka
db: batch=85, k=10, 2 10 2 58 2

SPT(16)	4305789918994247729	0 24 68 78 92 104 134 140 162 168 198 210 224 234 278 302	-818883998388
STPT(10)	4305790023722433677	0 2 54 56 72 74 90 92 144 146	-714155812440
TPT(14)	4305790033760585339	0 2 132 134 180 182 258 260 312 314 342 344 378 380	-704117660778
SPT(16)	4305790187912341049	0 38 50 98 138 168 242 330 350 438 512 542 582 630 642 680	-549965905068
SPT(16)	4305790232343155069	0 30 92 180 192 224 260 264 320 324 360 392 404 492 554 584	-505535091048
SPT(16)	4305790368024793981	0 22 42 46 78 90 112 172 246 306 328 340 372 376 396 418	-369853452136
TPT(14)	4305790773009724127	0 2 42 44 132 134 150 152 174 176 252 254 264 266	35131478010
SPT(16)	4305790965468222367	0 42 70 96 112 130 166 252 340 426 462 480 496 522 550 592	227589976250
SPT(16)	4305791600560292377	0 10 34 72 94 100 132 190 204 262 294 300 322 360 384 394	862682046260
SPT(18)	4305792180130679617	0 22 106 130 136 186 214 222 250 276 304 312 340 390 396 420 504 526	1442252433500
SPT(16)	4305793212189550793	0 6 26 50 56 78 96 110 126 140 158 180 186 210 230 236	2474311304676