Prime p₀= 2725947345251930711 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
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: 38
Found by: Cruncher Pete
db: batch=82, k=10, 2 4 2 10 2

SPT(16)	2725945412422334579	0 2 24 38 92 98 114 140 192 218 234 240 294 308 330 332	-1932829596132
STPT(10)	2725945466692341329	0 2 18 20 60 62 102 104 120 122	-1878559589382
SPT(16)	2725945469248805971	0 48 52 66 72 88 186 226 252 292 390 406 412 426 430 478	-1876003124740
SPT(16)	2725945751802771053	0 26 78 110 134 176 248 264 290 306 378 420 444 476 528 554	-1593449159658
STPT(10)	2725945961728230287	0 2 12 14 72 74 132 134 144 146	-1383523700424
STPT(10)	2725947213017321471	0 2 6 8 48 50 90 92 96 98	-132234609240
SPT(13)	2725948354979534851	0 36 48 66 78 90 108 126 138 150 168 180 216	1009727604140
SPT(16)	2725948400466536989	0 28 30 42 72 108 112 118 144 150 154 190 220 232 234 262	1055214606278
STPT(12)	2725949302478219141	0 2 30 32 60 62 126 128 156 158 186 188	1957226288430
SPT(16)	2725949310479303669	0 74 104 150 180 222 224 270 314 360 362 404 434 480 510 584	1965227372958
SPT(16)	2725949419034108299	0 58 70 88 138 180 240 244 378 382 442 484 534 552 564 622	2073782177588