Prime p₀= 1246956493174731509 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: emoga
db: batch=77, k=10, 2 40 2 16 2

SPT(16)	1246954725830700833	0 8 38 56 78 84 104 108 146 150 170 176 198 216 246 254	-1767344030676
STPT(10)	1246954948826475149	0 2 18 20 30 32 42 44 60 62	-1544348256360
SPT(16)	1246955067361905131	0 2 6 20 96 102 138 158 180 200 236 242 318 332 336 338	-1425812826378
STPT(10)	1246956188848359131	0 2 6 8 18 20 30 32 36 38	-304326372378
SPT(16)	1246956442831470703	0 10 48 70 90 156 208 210 376 378 430 496 516 538 576 586	-50343260806
SPT(16)	1246956482523809401	0 12 22 28 78 82 102 130 138 166 186 190 240 246 256 268	-10650922108
SPT(16)	1246956626168598637	0 6 42 70 84 94 106 190 276 360 372 382 396 424 460 466	132993867128
SPT(16)	1246956674429480771	0 30 80 92 96 102 110 120 158 168 176 182 186 198 248 278	181254749262
STPT(10)	1246956826595474087	0 2 30 32 60 62 90 92 120 122	333420742578
SPT(16)	1246956935278417387	0 16 30 34 72 76 142 156 220 234 300 304 342 346 360 376	442103685878
STPT(10)	1246957426271712497	0 2 24 26 42 44 60 62 84 86	933096980988