Prime p₀= 1241059489776239867 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 84 86
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: 86
Found by: Cruncher Pete
db: batch=77, k=10, 2 22 2 16 2

TPT(14)	1241058651185129717	0 2 12 14 54 56 150 152 180 182 330 332 420 422	-838591110150
SPT(18)	1241058730061306371	0 42 66 108 166 178 180 232 238 300 306 358 360 372 430 472 496 538	-759714933496
SPT(16)	1241058825999288301	0 10 40 66 76 82 90 96 166 172 180 186 196 222 252 262	-663776951566
SPT(16)	1241059024555068737	0 20 30 72 96 102 152 264 272 384 434 440 464 506 516 536	-465221171130
SPT(16)	1241059152302149049	0 8 72 122 182 200 204 228 434 458 462 480 540 590 654 662	-337474090818
SPT(16)	1241059222231369939	0 24 28 54 82 114 124 132 160 168 178 210 238 264 268 292	-267544869928
SPT(16)	1241059540233272197	0 36 42 54 84 96 102 106 120 124 130 142 172 184 190 226	50457032330
STPT(10)	1241059577454723779	0 2 18 20 30 32 42 44 60 62	87678483912
SPT(16)	1241059606315772053	0 4 30 40 66 88 156 178 186 208 276 298 324 334 360 364	116539532186
STPT(10)	1241059608468482219	0 2 18 20 30 32 42 44 60 62	118692242352
STPT(10)	1241059855378848257	0 2 30 32 42 44 54 56 84 86	365602608390