Prime p₀= 2338646111508246779 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 76 2 46 2 22 2 64 2 (?)
a_n: 0 2 30 32 72 74 150 152 198 200 222 224 288 290
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: 290
Found by: Landjunge
db: batch=81, k=14, 28 40 76 46 22 64

SPT(16)	2338644740665552433	0 14 36 44 50 78 116 174 200 258 296 324 330 338 360 374	-1370842694346
SPT(16)	2338644747267302237	0 14 32 80 140 144 170 194 210 234 260 264 324 372 390 404	-1364240944542
SPT(16)	2338645299435429053	0 24 86 90 150 216 240 264 266 290 314 380 440 444 506 530	-812072817726
SPT(16)	2338645523434147601	0 38 92 108 120 156 176 182 186 192 212 248 260 276 330 368	-588074099178
SPT(16)	2338645855973170999	0 10 22 28 54 100 124 198 244 318 342 388 414 420 432 442	-255535075780
SPT(16)	2338645893026738671	0 18 22 36 70 82 126 190 228 292 336 348 382 396 400 418	-218481508108
STPT(10)	2338646213451103679	0 2 12 14 30 32 48 50 60 62	101942856900
TPT(14)	2338646309522186429	0 2 78 80 132 134 318 320 330 332 342 344 360 362	198013939650
TPT(14)	2338646661822901007	0 2 42 44 54 56 144 146 420 422 492 494 504 506	550314654228
SPT(16)	2338646921942189797	0 4 60 94 126 130 144 154 186 196 210 214 246 280 336 340	810433943018
SPT(16)	2338646997387755963	0 30 38 68 80 98 108 110 186 188 198 216 228 258 266 296	885879509184