Prime p₀= 865639520674313081 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 130 2 28 2 70 2 58 2 34 2 (?)
a_n: 0 2 6 8 138 140 168 170 240 242 300 302 336 338
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: 338
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 4 130 28 70 58 34

SPT(16)	865638089593743959	0 8 20 48 54 80 110 122 150 162 192 218 224 252 264 272	-1431080569122
STPT(10)	865638283676378999	0 2 42 44 90 92 138 140 180 182	-1236997934082
SPT(16)	865638370931319431	0 32 42 50 62 68 80 90 110 120 132 138 150 158 168 200	-1149742993650
SPT(16)	865638631572479543	0 6 56 60 84 104 116 140 150 174 186 206 230 234 284 290	-889101833538
SPT(16)	865638742018604989	0 24 28 30 84 102 108 138 154 184 190 208 262 264 268 292	-778655708092
SPT(16)	865639473926513717	0 12 44 54 60 72 114 144 182 212 254 266 272 282 314 326	-46747799364
SPT(16)	865639772219321521	0 28 42 76 132 148 156 192 196 232 240 256 312 346 360 388	251545008440
STPT(10)	865639838398654127	0 2 54 56 72 74 90 92 144 146	317724341046
TPT(14)	865639956604774259	0 2 30 32 42 44 60 62 102 104 138 140 150 152	435930461178
STPT(10)	865639977944842151	0 2 6 8 18 20 30 32 36 38	457270529070
SPT(16)	865640131435650983	0 14 18 24 38 44 66 80 174 188 210 216 230 236 240 254	610761337902