Prime p₀= 1951503806365421849 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 100 2 4 2 100 2 16 2 22 2 (?)
a_n: 0 2 60 62 162 164 168 170 270 272 288 290 312 314
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: 314
Found by: Orange Kid
db: batch=80, k=14, 58 100 4 100 16 22

SPT(16)	1951502417683802861	0 36 72 78 80 152 180 182 246 248 276 348 350 356 392 428	-1388681618988
STPT(10)	1951503099013326707	0 2 30 32 60 62 90 92 120 122	-707352095142
SPT(16)	1951503294271850437	0 10 30 34 66 82 96 100 126 130 144 160 192 196 216 226	-512093571412
TPT(14)	1951503528159184157	0 2 30 32 42 44 54 56 132 134 264 266 312 314	-278206237692
SPT(16)	1951503713227842929	0 24 68 72 78 128 134 140 192 198 204 254 260 264 308 332	-93137578920
STPT(10)	1951503798079049969	0 2 18 20 30 32 42 44 60 62	-8286371880
SPT(16)	1951504079233445887	0 22 34 36 52 54 96 132 154 190 232 234 250 252 264 286	272868024038
STPT(10)	1951504170794509997	0 2 30 32 42 44 54 56 84 86	364429088148
SPT(16)	1951504281481115861	0 38 68 108 128 152 162 198 230 266 276 300 320 360 390 428	475115694012
STPT(10)	1951504681517811317	0 2 60 62 72 74 84 86 144 146	875152389468
SPT(16)	1951504825821944977	0 22 64 70 100 136 154 166 180 192 210 246 276 282 324 346	1019456523128