Prime p₀= 1286353955491050317 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 124 2 10 2 58 2 16 2 40 2 (?)
a_n: 0 2 84 86 210 212 222 224 282 284 300 302 342 344
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: 344
Found by: mikey
db: batch=77, k=14, 82 124 10 58 16 40

SPT(16)	1286352586469130049	0 22 34 58 78 84 90 114 148 172 178 184 204 228 240 262	-1369021920268
STPT(10)	1286353042400135621	0 2 6 8 18 20 30 32 36 38	-913090914696
SPT(16)	1286353492975797011	0 12 20 50 62 68 78 80 108 110 120 126 138 168 176 188	-462515253306
SPT(16)	1286353744369813799	0 44 78 92 110 128 168 170 192 194 234 252 270 284 318 362	-211121236518
SPT(16)	1286353802855386781	0 18 42 50 66 68 98 102 116 120 150 152 168 176 200 218	-152635663536
STPT(10)	1286353845051937547	0 2 30 32 72 74 114 116 144 146	-110439112770
SPT(16)	1286354071766540093	0 18 20 158 188 206 240 254 270 284 318 336 366 504 506 524	116275489776
STPT(10)	1286354078383134749	0 2 18 20 30 32 42 44 60 62	122892084432
STPT(10)	1286354095630993691	0 2 30 32 78 80 126 128 156 158	140139943374
STPT(10)	1286354535362166167	0 2 30 32 102 104 174 176 204 206	579871115850
SPT(16)	1286354619338100241	0 18 28 42 108 118 132 150 178 196 210 220 286 300 310 328	663847049924