Prime p₀= 2117777144114101409 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 28 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 90 92 120 122
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: 122
Found by: gemini8
db: batch=80, k=10, 2 28 2 28 2

SPT(18)	2117774900114268103	0 24 64 78 220 228 244 258 274 300 316 330 346 354 496 510 550 574	-2243999833306
SPT(16)	2117775815196993143	0 14 66 80 90 108 128 150 194 216 236 254 264 278 330 344	-1328917108266
SPT(18)	2117776016572038751	0 10 42 48 52 60 78 82 102 196 216 220 238 246 250 256 288 298	-1127542062658
STPT(10)	2117776132003207757	0 2 12 14 72 74 132 134 144 146	-1012110893652
SPT(16)	2117776829900968751	0 56 110 116 140 146 152 186 302 336 342 348 372 378 432 488	-314213132658
SPT(18)	2117777060787317899	0 12 40 58 72 84 100 142 160 162 180 222 238 250 264 282 310 322	-83326783510
SPT(16)	2117777410750360963	0 24 58 60 90 114 130 160 168 198 214 238 268 270 304 328	266636259554
TPT(14)	2117777654723094107	0 2 30 32 72 74 120 122 144 146 174 176 210 212	510608992698
SPT(16)	2117777690492834057	0 20 36 42 84 122 156 174 242 260 294 332 374 380 396 416	546378732648
STPT(10)	2117777912259388409	0 2 18 20 30 32 42 44 60 62	768145287000
STPT(10)	2117778421403774159	0 2 18 20 30 32 42 44 60 62	1277289672750