Prime p₀= 1041401126964756749 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 28 2 22 2 16 2 148 2 40 2 (?)
a_n: 0 2 48 50 78 80 102 104 120 122 270 272 312 314
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: 314
Found by: [AF>Libristes]Maeda
db: batch=76, k=14, 46 28 22 16 148 40

SPT(16)	1041398197581715409	0 2 30 42 60 78 182 198 212 228 332 350 368 380 408 410	-2929383041340
TPT(14)	1041398938122583739	0 2 18 20 180 182 240 242 318 320 402 404 408 410	-2188842173010
SPT(16)	1041399371313038251	0 12 28 70 78 82 100 108 112 120 138 142 150 192 208 220	-1755651718498
STPT(10)	1041400804442860889	0 2 18 20 30 32 42 44 60 62	-322521895860
SPT(16)	1041400850891906179	0 34 48 52 70 100 108 112 120 124 132 162 180 184 198 232	-276072850570
STPT(10)	1041401124153493247	0 2 42 44 72 74 102 104 144 146	-2811263502
SPT(16)	1041401396691303247	0 4 36 46 70 94 120 124 132 136 162 186 210 220 252 256	269726546498
SPT(16)	1041401399093936599	0 10 42 54 82 88 102 112 270 280 294 300 328 340 372 382	272129179850
SPT(16)	1041401403594931501	0 6 52 66 90 126 180 196 222 238 292 328 352 366 412 418	276630174752
STPT(10)	1041401937187906109	0 2 12 14 30 32 48 50 60 62	810223149360
SPT(16)	1041401944978305413	0 48 66 84 86 104 116 158 306 348 360 378 380 398 416 464	818013548664