Prime p₀= 1007648249285073161 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 118 2 10 2 118 2 46 2 22 2 (?)
a_n: 0 2 6 8 126 128 138 140 258 260 306 308 330 332
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: 332
Found by: gemini8
db: batch=76, k=14, 4 118 10 118 46 22

SPT(16)	1007647584578484293	0 14 20 44 48 68 80 114 230 264 276 296 300 324 330 344	-664706588868
TPT(14)	1007647608697262021	0 2 60 62 108 110 150 152 168 170 210 212 228 230	-640587811140
SPT(16)	1007647981632444013	0 30 70 130 136 148 154 190 234 270 276 288 294 354 394 424	-267652629148
SPT(16)	1007648057846587609	0 12 22 58 64 118 132 160 162 190 204 258 264 300 310 322	-191438485552
STPT(10)	1007648065272583349	0 2 18 20 30 32 42 44 60 62	-184012489812
TPT(14)	1007648178084710051	0 2 66 68 108 110 138 140 180 182 198 200 246 248	-71200363110
SPT(16)	1007648388893508139	0 12 22 40 42 52 100 114 178 192 240 250 252 270 280 292	139608434978
TPT(14)	1007648847907453331	0 2 30 32 108 110 126 128 150 152 186 188 336 338	598622380170
SPT(16)	1007648901457057903	0 10 36 40 58 64 114 150 154 190 240 246 264 268 294 304	652171984742
SPT(16)	1007649499861202659	0 4 10 52 60 90 112 114 130 132 154 184 192 234 240 244	1250576129498
SPT(16)	1007649917679949639	0 54 72 102 138 142 168 174 208 214 240 244 280 310 328 382	1668394876478