Prime p₀= 3017024721634679729 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 46 2 28 2 58 2 70 2 124 2 (?)
a_n: 0 2 72 74 120 122 150 152 210 212 282 284 408 410
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-FC] hl
db: batch=82, k=14, 70 46 28 58 70 124

SPT(16)	3017023174968875353	0 24 28 30 58 64 100 120 178 198 234 240 268 270 274 298	-1546665804376
SPT(16)	3017023834615977469	0 28 70 84 154 162 178 220 222 264 280 288 358 372 414 442	-887018702260
SPT(16)	3017023882796382923	0 66 98 104 116 120 140 150 224 234 254 258 270 276 308 374	-838838296806
STPT(10)	3017024018594522141	0 2 6 8 18 20 30 32 36 38	-703040157588
SPT(16)	3017024287600415159	0 8 14 20 30 62 132 144 158 170 240 272 282 288 294 302	-434034264570
SPT(16)	3017024695831962457	0 36 96 120 136 180 244 246 250 252 316 360 376 400 460 496	-25802717272
SPT(16)	3017024927423509999	0 12 28 34 72 112 118 154 168 204 210 250 288 294 310 322	205788830270
TPT(14)	3017025099823404809	0 2 12 14 18 20 60 62 168 170 198 200 228 230	378188725080
SPT(16)	3017025140883170743	0 18 34 36 88 118 120 130 144 154 156 186 238 240 256 274	419248491014
STPT(10)	3017025748893833177	0 2 54 56 72 74 90 92 144 146	1027259153448
TPT(14)	3017025960465580109	0 2 72 74 102 104 132 134 168 170 252 254 258 260	1238830900380