Prime p₀= 2046875691901396439 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 208 2 40 2 226 2 10 2 148 2 16 2 (?)
a_n: 0 2 210 212 252 254 480 482 492 494 642 644 660 662
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: 662
Found by: JonS
db: batch=80, k=14, 208 40 226 10 148 16

SPT(16)	2046874571013197671	0 16 22 30 42 70 76 100 102 126 132 160 172 180 186 202	-1120888198768
SPT(16)	2046874823482857821	0 38 48 50 102 110 180 182 186 188 258 266 318 320 330 368	-868418538618
SPT(16)	2046874990350826073	0 8 54 74 78 86 120 146 168 194 228 236 240 260 306 314	-701550570366
SPT(16)	2046875015881932319	0 12 40 52 88 94 102 118 144 160 168 174 210 222 250 262	-676019464120
SPT(16)	2046875096039968543	0 4 24 46 60 66 76 94 126 144 154 160 174 196 216 220	-595861427896
SPT(16)	2046875584904878181	0 12 42 48 62 68 72 90 110 128 132 138 152 158 188 200	-106996518258
SPT(16)	2046875929267143241	0 36 72 106 108 178 226 232 276 282 330 400 402 436 472 508	237365746802
SPT(16)	2046875996837073439	0 48 60 90 100 142 168 192 220 244 270 312 322 352 364 412	304935677000
SPT(16)	2046876458986219583	0 24 38 60 84 98 116 120 254 258 276 290 314 336 350 374	767084823144
SPT(16)	2046877076549082263	0 26 30 38 84 96 176 180 194 198 278 290 336 344 348 374	1384647685824
TPT(14)	2046877224752832137	0 2 54 56 120 122 150 152 180 182 240 242 252 254	1532851435698