Prime p₀= 1295707187462661287 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 10 2 88 2 76 2 16 2 10 2 (?)
a_n: 0 2 42 44 54 56 144 146 222 224 240 242 252 254
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: 254
Found by: Cruncher Pete
db: batch=77, k=14, 40 10 88 76 16 10

SPT(16)	1295706193548395633	0 8 36 104 114 138 144 156 158 170 176 200 210 278 306 314	-993914265654
SPT(16)	1295706396306808841	0 32 38 56 66 150 168 176 192 200 218 302 312 330 336 368	-791155852446
SPT(16)	1295706438912961079	0 2 32 42 54 72 78 92 120 134 140 158 170 180 210 212	-748549700208
STPT(10)	1295706490244288621	0 2 36 38 78 80 120 122 156 158	-697218372666
STPT(10)	1295706717123398519	0 2 42 44 60 62 78 80 120 122	-470339262768
SPT(16)	1295707061458071289	0 4 18 102 112 118 150 174 178 202 234 240 250 334 348 352	-126004589998
TPT(14)	1295707260764902079	0 2 42 44 78 80 120 122 132 134 150 152 162 164	73302240792
SPT(16)	1295707568967544027	0 12 40 42 84 126 136 166 180 210 220 262 304 306 334 346	381504882740
STPT(10)	1295707621381928327	0 2 24 26 42 44 60 62 84 86	433919267040
SPT(16)	1295707650287506177	0 10 24 30 52 64 66 156 190 280 282 294 316 322 336 346	462824844890
SPT(16)	1295707726932268619	0 2 14 48 74 84 90 102 170 182 188 198 224 258 270 272	539469607332