Prime p₀= 2506542289391678267 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 40 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 114 116 144 146
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: [AF>Linux]Rogue 9
db: batch=82, k=10, 2 28 2 40 2

TPT(16)	2506541330194418129	0 2 18 20 90 92 132 134 228 230 240 242 312 314 348 350	-959197260138
STPT(10)	2506541491045372367	0 2 30 32 72 74 114 116 144 146	-798346305900
SPT(16)	2506541702967158953	0 6 18 28 48 78 94 96 118 120 136 166 186 196 208 214	-586424519314
SPT(16)	2506541720764773551	0 18 80 122 138 182 270 278 312 320 408 452 468 510 572 590	-568626904716
SPT(20)	2506542105930844133	0 26 66 84 116 126 140 168 218 248 306 336 386 414 428 438 470 488 528 554	-183460834134
SPT(16)	2506542235608657019	0 22 28 60 90 160 180 184 228 232 252 322 352 384 390 412	-53783021248
STPT(10)	2506542605891646821	0 2 36 38 78 80 120 122 156 158	316499968554
SPT(16)	2506542847685014067	0 62 74 86 102 122 140 146 150 156 174 194 210 222 234 296	558293335800
STPT(10)	2506542910057359419	0 2 30 32 120 122 210 212 240 242	620665681152
STPT(10)	2506543045846474487	0 2 30 32 72 74 114 116 144 146	756454796220
STPT(10)	2506543316747225051	0 2 6 8 18 20 30 32 36 38	1027355546784