Prime p₀= 865639956604774259 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 40 2 34 2 10 2 (?)
a_n: 0 2 30 32 42 44 60 62 102 104 138 140 150 152
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: 152
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 28 10 16 40 34 10

SPT(16)	865638631572479543	0 6 56 60 84 104 116 140 150 174 186 206 230 234 284 290	-1325032294716
SPT(16)	865638742018604989	0 24 28 30 84 102 108 138 154 184 190 208 262 264 268 292	-1214586169270
SPT(16)	865639473926513717	0 12 44 54 60 72 114 144 182 212 254 266 272 282 314 326	-482678260542
TPT(14)	865639520674313081	0 2 6 8 138 140 168 170 240 242 300 302 336 338	-435930461178
SPT(16)	865639772219321521	0 28 42 76 132 148 156 192 196 232 240 256 312 346 360 388	-184385452738
STPT(10)	865639838398654127	0 2 54 56 72 74 90 92 144 146	-118206120132
STPT(10)	865639977944842151	0 2 6 8 18 20 30 32 36 38	21340067892
SPT(16)	865640131435650983	0 14 18 24 38 44 66 80 174 188 210 216 230 236 240 254	174830876724
TPT(14)	865640308392529721	0 2 126 128 210 212 216 218 228 230 336 338 408 410	351787755462
SPT(16)	865640429366067167	0 2 36 66 92 102 134 140 186 192 224 234 260 290 324 326	472761292908
STPT(10)	865640560619406917	0 2 42 44 72 74 102 104 144 146	604014632658