Prime p₀= 1297148668755649649 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 16 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 78 80 120 122
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: Cruncher Pete
db: batch=77, k=10, 2 40 2 16 2

STPT(10)	1297147291515572597	0 2 60 62 72 74 84 86 144 146	-1377240077052
SPT(16)	1297147344240703843	0 6 60 96 160 186 240 270 364 394 448 474 538 574 628 634	-1324514945806
SPT(16)	1297147423947161749	0 18 30 48 72 102 112 130 210 228 238 268 292 310 322 340	-1244808487900
SPT(16)	1297147773585677219	0 30 38 72 78 90 98 122 138 162 170 182 188 222 230 260	-895169972430
STPT(10)	1297148384733965591	0 2 36 38 78 80 120 122 156 158	-284021684058
SPT(16)	1297148439097872167	0 2 6 44 66 104 126 132 164 170 192 230 252 290 294 296	-229657777482
STPT(10)	1297148731792576847	0 2 30 32 60 62 90 92 120 122	63036927198
STPT(10)	1297149206538417677	0 2 30 32 42 44 54 56 84 86	537782768028
SPT(16)	1297149634332075499	0 22 42 82 108 132 178 198 202 222 268 292 318 358 378 400	965576425850
STPT(10)	1297150214664588371	0 2 6 8 48 50 90 92 96 98	1545908938722
TPT(14)	1297150245223328759	0 2 90 92 198 200 240 242 258 260 282 284 468 470	1576467679110