Prime p₀= 1235321508116022317 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 28 2 28 2 40 2 (?)
a_n: 0 2 42 44 72 74 102 104 144 146
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: Cruncher Pete
db: batch=77, k=10, 2 40 2 28 2

SPT(16)	1235321126672185571	0 2 110 168 210 212 240 260 288 308 336 338 380 438 546 548	-381443836746
SPT(16)	1235321137909473871	0 18 46 48 88 102 120 156 172 208 226 240 280 282 310 328	-370206548446
SPT(16)	1235321147354030029	0 54 90 112 142 144 234 258 304 328 418 420 450 472 508 562	-360761992288
STPT(10)	1235321296225551677	0 2 72 74 102 104 132 134 204 206	-211890470640
STPT(10)	1235321382945150269	0 2 18 20 30 32 42 44 60 62	-125170872048
STPT(10)	1235321432045054141	0 2 126 128 168 170 210 212 336 338	-76070968176
SPT(16)	1235322144823928111	0 20 30 32 42 56 80 90 98 108 132 146 156 158 168 188	636707905794
STPT(10)	1235322259046983097	0 2 42 44 72 74 102 104 144 146	750930960780
SPT(16)	1235322412836220067	0 56 84 156 170 186 204 260 276 332 350 366 380 452 480 536	904720197750
SPT(16)	1235322832624692937	0 42 90 102 184 244 262 292 354 384 402 462 544 556 604 646	1324508670620
TPT(14)	1235323177726508369	0 2 30 32 72 74 78 80 132 134 198 200 210 212	1669610486052