Prime p₀= 1251419019631647989 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 46 2 40 2 40 2 46 2 (?)
a_n: 0 2 48 50 90 92 132 134 180 182
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: 182
Found by: Cruncher Pete
db: batch=77, k=10, 2 46 2 40 2

STPT(12)	1251418428402782357	0 2 12 14 54 56 90 92 132 134 144 146	-591228865632
SPT(20)	1251418645374341309	0 48 60 62 92 98 158 188 192 194 258 260 264 294 354 360 390 392 404 452	-374257306680
SPT(16)	1251418645950770347	0 24 52 84 94 102 124 130 144 150 172 180 190 222 250 274	-373680877642
SPT(16)	1251418706867870909	0 8 14 32 42 68 134 162 200 228 294 320 330 348 354 362	-312763777080
STPT(10)	1251418835958639377	0 2 12 14 42 44 72 74 84 86	-183673008612
SPT(16)	1251419010182679427	0 4 6 102 144 172 174 202 264 292 294 322 364 460 462 466	-9448968562
STPT(10)	1251419734491768227	0 2 12 14 42 44 72 74 84 86	714860120238
SPT(16)	1251419852524445363	0 78 84 128 134 146 188 200 354 366 408 420 426 470 476 554	832892797374
SPT(16)	1251419973386440997	0 2 14 20 96 132 144 146 150 152 164 200 276 282 294 296	953754793008
SPT(16)	1251420141266615647	0 54 82 96 120 130 150 162 364 376 396 406 430 444 472 526	1121634967658
STPT(10)	1251420154401954527	0 2 12 14 72 74 132 134 144 146	1134770306538