Prime p₀= 865640308392529721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 82 2 4 2 10 2 106 2 70 2 (?)
a_n: 0 2 126 128 210 212 216 218 228 230 336 338 408 410
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: 410
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 124 82 4 10 106 70

TPT(14)	865639520674313081	0 2 6 8 138 140 168 170 240 242 300 302 336 338	-787718216640
SPT(16)	865639772219321521	0 28 42 76 132 148 156 192 196 232 240 256 312 346 360 388	-536173208200
STPT(10)	865639838398654127	0 2 54 56 72 74 90 92 144 146	-469993875594
TPT(14)	865639956604774259	0 2 30 32 42 44 60 62 102 104 138 140 150 152	-351787755462
STPT(10)	865639977944842151	0 2 6 8 18 20 30 32 36 38	-330447687570
SPT(16)	865640131435650983	0 14 18 24 38 44 66 80 174 188 210 216 230 236 240 254	-176956878738
SPT(16)	865640429366067167	0 2 36 66 92 102 134 140 186 192 224 234 260 290 324 326	120973537446
STPT(10)	865640560619406917	0 2 42 44 72 74 102 104 144 146	252226877196
SPT(16)	865640602740716893	0 6 16 30 48 60 76 90 124 138 154 166 184 198 208 214	294348187172
SPT(16)	865641216202908533	0 50 78 98 188 240 258 308 330 380 398 450 540 560 588 638	907810378812
SPT(16)	865641345201826331	0 32 36 50 56 132 176 210 242 276 320 396 402 416 420 452	1036809296610