Prime p₀= 3017965421202130871 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 58 2 10 2 70 2 76 2 40 2 (?)
a_n: 0 2 36 38 96 98 108 110 180 182 258 260 300 302
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: 302
Found by: [SG-FC] hl
db: batch=82, k=14, 34 58 10 70 76 40

SPT(16)	3017964018501798013	0 18 30 36 88 118 126 130 156 160 168 198 250 256 268 286	-1402700332858
SPT(16)	3017964513578798767	0 12 40 42 64 70 76 90 106 120 126 132 154 156 184 196	-907623332104
SPT(16)	3017964534575949713	0 86 150 170 174 186 216 264 326 374 404 416 420 440 504 590	-886626181158
STPT(10)	3017964645579746867	0 2 42 44 132 134 222 224 264 266	-775622384004
TPT(14)	3017964648870655619	0 2 42 44 102 104 378 380 408 410 420 422 438 440	-772331475252
STPT(10)	3017964901721389559	0 2 18 20 30 32 42 44 60 62	-519480741312
SPT(16)	3017966339518602763	0 4 16 18 30 36 58 84 100 126 148 154 166 168 180 184	918316471892
SPT(16)	3017966512204003933	0 6 30 46 48 84 94 114 130 150 160 196 198 214 238 244	1091001873062
SPT(16)	3017967060210700099	0 22 52 64 94 118 130 154 168 192 204 228 258 270 300 322	1639008569228
SPT(16)	3017967506971467019	0 4 40 54 58 78 114 124 228 238 274 294 298 312 348 352	2085769336148
STPT(10)	3017967677654798987	0 2 30 32 42 44 54 56 84 86	2256452668116