Prime p₀= 1376587872613630421 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 178 2 106 2 28 2 16 2 40 2 46 2 (?)
a_n: 0 2 180 182 288 290 318 320 336 338 378 380 426 428
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: 428
Found by: [SG-2W]Kurzer
db: batch=77, k=14, 178 106 28 16 40 46

SPT(16)	1376586871602778657	0 24 34 76 90 112 142 196 240 294 324 346 360 402 412 436	-1001010851764
STPT(10)	1376586991733948177	0 2 30 32 42 44 54 56 84 86	-880879682244
SPT(16)	1376587464239032147	0 16 22 40 64 90 100 126 160 186 196 222 246 264 270 286	-408374598274
STPT(10)	1376587533284942357	0 2 30 32 42 44 54 56 84 86	-339328688064
SPT(16)	1376587698536141887	0 52 60 66 70 82 112 124 132 144 174 186 190 196 204 256	-174077488534
SPT(20)	1376587857550020851	0 30 32 36 60 66 86 102 120 150 218 248 266 282 302 308 332 336 338 368	-15063609570
TPT(14)	1376588124946761281	0 2 36 38 78 80 90 92 156 158 228 230 300 302	252333130860
STPT(10)	1376588144145610211	0 2 6 8 48 50 90 92 96 98	271531979790
TPT(14)	1376588194685791931	0 2 138 140 156 158 180 182 198 200 258 260 306 308	322072161510
SPT(16)	1376588307537356279	0 32 44 80 92 108 114 150 182 218 224 240 252 288 300 332	434923725858
SPT(16)	1376588429066052689	0 42 50 84 90 114 152 222 260 330 368 392 398 432 440 482	556452422268