Prime p₀= 1406567391066836657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 16 2 40 2 28 2 88 2 16 2 (?)
a_n: 0 2 24 26 42 44 84 86 114 116 204 206 222 224
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: 224
Found by: bfromcolo
db: batch=78, k=14, 22 16 40 28 88 16

SPT(16)	1406566279432820239	0 4 18 42 100 118 138 184 198 244 264 282 340 364 378 382	-1111634016418
TPT(14)	1406566676555878307	0 2 30 32 54 56 72 74 84 86 114 116 120 122	-714510958350
SPT(16)	1406566740732782149	0 24 48 52 82 100 132 138 154 160 192 210 240 244 268 292	-650334054508
SPT(20)	1406566868470645061	0 36 38 42 56 96 140 152 176 192 206 222 246 258 302 342 356 360 362 398	-522596191596
STPT(10)	1406566937282659499	0 2 42 44 90 92 138 140 180 182	-453784177158
STPT(12)	1406567162637974969	0 2 60 62 78 80 210 212 228 230 288 290	-228428861688
SPT(16)	1406567427191766013	0 6 94 130 174 184 196 220 234 258 270 280 324 360 448 454	36124929356
SPT(16)	1406567528264161903	0 24 30 34 40 118 124 150 184 210 216 294 300 304 310 334	137197325246
SPT(16)	1406567798999646067	0 16 22 24 36 64 130 184 192 246 312 340 352 354 360 376	407932809410
STPT(10)	1406567954824532411	0 2 6 8 18 20 30 32 36 38	563757695754
STPT(10)	1406568141315955859	0 2 42 44 90 92 138 140 180 182	750249119202