Prime p₀= 1296896496312255659 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(12)	1296894700238370587	0 2 12 14 54 56 90 92 132 134 144 146	-1796073885072
SPT(16)	1296894957177096281	0 2 12 26 56 86 90 92 96 98 102 132 162 176 186 188	-1539135159378
SPT(16)	1296894994273196959	0 40 42 64 78 112 138 172 180 214 240 274 288 310 312 352	-1502039058700
STPT(10)	1296895512806960291	0 2 36 38 78 80 120 122 156 158	-983505295368
SPT(16)	1296895872878259691	0 70 78 148 160 168 202 300 310 408 442 450 462 532 540 610	-623433995968
STPT(10)	1296895891630165427	0 2 30 32 42 44 54 56 84 86	-604682090232
SPT(16)	1296896876618874673	0 48 94 114 126 130 168 226 228 286 324 328 340 360 406 454	380306619014
STPT(10)	1296896949288669107	0 2 30 32 42 44 54 56 84 86	452976413448
STPT(10)	1296897775100446469	0 2 18 20 30 32 42 44 60 62	1278788190810
SPT(16)	1296897859312207237	0 12 52 72 94 126 180 184 192 196 250 282 304 324 364 376	1362999951578
STPT(10)	1296897931637831987	0 2 90 92 102 104 114 116 204 206	1435325576328