Prime p₀= 729491583046429781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 22 2 16 2 148 2 16 2 52 2 (?)
a_n: 0 2 6 8 30 32 48 50 198 200 216 218 270 272
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 272
Found by: Theadalus
db: batch=73, k=14, 4 22 16 148 16 52

SPT(16)	729491294589516643	0 4 6 28 70 78 100 118 156 174 196 204 246 268 270 274	-288456913138
TPT(14)	729491379941436029	0 2 12 14 30 32 78 80 108 110 168 170 210 212	-203104993752
TPT(14)	729491430413101787	0 2 54 56 60 62 90 92 144 146 324 326 354 356	-152633327994
SPT(16)	729491503529123539	0 12 28 40 42 78 112 190 210 288 322 358 360 372 388 400	-79517306242
SPT(16)	729491517285983041	0 6 66 126 130 132 150 156 232 238 256 258 262 322 382 388	-65760446740
STPT(10)	729491533928628431	0 2 36 38 78 80 120 122 156 158	-49117801350
SPT(16)	729491700271671529	0 10 24 40 48 82 100 114 118 132 150 184 192 208 222 232	117225241748
STPT(10)	729491939341232831	0 2 30 32 78 80 126 128 156 158	356294803050
SPT(16)	729492158508726611	0 42 48 92 138 140 152 162 206 216 228 230 276 320 326 368	575462296830
STPT(10)	729492526667229077	0 2 30 32 42 44 54 56 84 86	943620799296
STPT(10)	729492755406702641	0 2 6 8 48 50 90 92 96 98	1172360272860