Prime p₀= 1427427380318440469 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 94 2 238 2 10 2 76 2 70 2 (?)
a_n: 0 2 42 44 138 140 378 380 390 392 468 470 540 542
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: 542
Found by: matali
db: batch=78, k=14, 40 94 238 10 76 70

SPT(18)	1427427072566287447	0 6 36 76 90 102 144 166 180 196 210 232 274 286 300 340 370 376	-307752153022
STPT(10)	1427427106023948851	0 2 6 8 48 50 90 92 96 98	-274294491618
TPT(14)	1427427131623910201	0 2 168 170 210 212 276 278 306 308 336 338 378 380	-248694530268
SPT(16)	1427427225581373559	0 28 78 90 112 138 148 160 162 174 184 210 232 244 294 322	-154737066910
SPT(16)	1427427296709739399	0 40 60 88 132 174 222 250 252 280 328 370 414 442 462 502	-83608701070
TPT(14)	1427427328344643889	0 2 42 44 90 92 180 182 282 284 420 422 480 482	-51973796580
STPT(10)	1427427426450863729	0 2 12 14 90 92 168 170 180 182	46132423260
SPT(16)	1427427427975447603	0 40 66 90 94 160 178 234 280 336 354 420 424 448 474 514	47657007134
SPT(16)	1427427473745614147	0 14 20 32 50 60 66 102 104 140 146 156 174 186 192 206	93427173678
SPT(18)	1427427720566096387	0 12 14 26 54 62 102 146 162 164 180 224 264 272 300 312 314 326	340247655918
SPT(16)	1427427900058661251	0 10 28 58 72 78 108 142 156 190 220 226 240 270 288 298	519740220782