Prime p₀= 782423075406968657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 40 2 196 2 28 2 10 2 (?)
a_n: 0 2 60 62 72 74 114 116 312 314 342 344 354 356
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: 356
Found by: [SG]steini
db: batch=73, k=14, 58 10 40 196 28 10

STPT(10)	782422308251849267	0 2 30 32 60 62 90 92 120 122	-767155119390
SPT(16)	782422600238403797	0 26 54 66 92 116 164 176 210 222 270 294 320 332 360 386	-475168564860
SPT(16)	782422604717528321	0 2 18 32 42 66 122 128 180 186 242 266 276 290 306 308	-470689440336
SPT(16)	782422693540703503	0 30 40 54 114 144 150 156 178 184 190 220 280 294 304 334	-381866265154
STPT(10)	782422764207011027	0 2 90 92 102 104 114 116 204 206	-311199957630
STPT(10)	782422964318015357	0 2 30 32 42 44 54 56 84 86	-111088953300
STPT(10)	782423574661843727	0 2 30 32 42 44 54 56 84 86	499254875070
TPT(14)	782423802988661609	0 2 12 14 72 74 150 152 252 254 270 272 282 284	727581692952
STPT(12)	782423995020833687	0 2 30 32 42 44 132 134 144 146 174 176	919613865030
SPT(16)	782424162939082817	0 14 20 24 44 54 62 80 114 132 140 150 170 174 180 194	1087532114160
SPT(16)	782424293800329529	0 24 72 112 114 138 154 172 180 198 214 238 240 280 328 352	1218393360872