Prime p₀= 1285862753367385439 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 76 2 58 2 28 2 28 2 (?)
a_n: 0 2 30 32 42 44 120 122 180 182 210 212 240 242
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: 242
Found by: Cruncher Pete
db: batch=77, k=14, 28 10 76 58 28 28

SPT(16)	1285861443256992169	0 10 22 40 52 54 78 100 162 184 208 210 222 240 252 262	-1310110393270
STPT(10)	1285861810133680457	0 2 60 62 72 74 84 86 144 146	-943233704982
STPT(10)	1285862220623902949	0 2 18 20 30 32 42 44 60 62	-532743482490
SPT(16)	1285862314290431057	0 36 50 56 102 122 126 180 332 386 390 410 456 462 476 512	-439076954382
SPT(16)	1285862449415456201	0 50 56 66 92 120 126 128 240 242 248 276 302 312 318 368	-303951929238
SPT(16)	1285862605478555591	0 6 18 56 116 152 158 170 198 210 216 252 312 350 362 368	-147888829848
SPT(16)	1285862948189505401	0 20 30 48 56 60 78 92 126 140 158 162 170 188 198 218	194822119962
STPT(10)	1285863325474893689	0 2 18 20 30 32 42 44 60 62	572107508250
STPT(10)	1285863480799088309	0 2 18 20 30 32 42 44 60 62	727431702870
TPT(14)	1285863553409875211	0 2 78 80 90 92 120 122 126 128 186 188 228 230	800042489772
SPT(16)	1285863669911491997	0 2 14 32 56 74 84 144 152 212 222 240 264 282 294 296	916544106558