Prime p₀= 3034547873958870569 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 136 2 40 2 76 2 70 2 16 2 (?)
a_n: 0 2 60 62 198 200 240 242 318 320 390 392 408 410
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]ATA-Rolf
db: batch=82, k=14, 58 136 40 76 70 16

SPT(16)	3034545471474634057	0 12 24 66 84 90 120 124 162 166 196 202 220 262 274 286	-2402484236512
STPT(10)	3034545544783955117	0 2 24 26 42 44 60 62 84 86	-2329174915452
SPT(16)	3034546011032018687	0 14 50 80 84 120 122 140 144 162 164 200 204 234 270 284	-1862926851882
SPT(16)	3034546489857185557	0 22 36 46 52 60 106 112 144 150 196 204 210 220 234 256	-1384101685012
SPT(16)	3034546865391567457	0 22 46 54 72 96 100 112 114 126 130 154 172 180 204 226	-1008567303112
SPT(16)	3034547673691459823	0 6 20 56 84 104 128 144 170 186 210 230 258 294 308 314	-200267410746
STPT(10)	3034547995132864097	0 2 30 32 42 44 54 56 84 86	121173993528
SPT(16)	3034548547425392663	0 8 26 30 78 84 86 96 98 108 110 116 164 168 186 194	673466522094
STPT(10)	3034548826814781737	0 2 24 26 42 44 60 62 84 86	952855911168
SPT(16)	3034549098475188139	0 18 42 60 82 108 138 150 172 184 214 240 262 280 304 322	1224516317570
SPT(16)	3034549200845496281	0 30 36 72 126 128 132 140 198 206 210 212 266 302 308 338	1326886625712