Prime p₀= 1038735258737019407 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 58 2 64 2 118 2 10 2 70 2 (?)
a_n: 0 2 54 56 114 116 180 182 300 302 312 314 384 386
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: 386
Found by: [SG-2W]Kurzer
db: batch=76, k=14, 52 58 64 118 10 70

SPT(16)	1038732875029043627	0 12 30 86 210 212 234 236 270 272 294 296 420 476 494 506	-2383707975780
SPT(16)	1038733070108308027	0 6 22 34 90 102 124 126 250 252 274 286 342 354 370 376	-2188628711380
SPT(16)	1038733114187780797	0 34 36 66 76 84 90 106 114 130 136 144 154 184 186 220	-2144549238610
STPT(10)	1038733671371695457	0 2 54 56 72 74 90 92 144 146	-1587365323950
STPT(10)	1038734254028127869	0 2 42 44 60 62 78 80 120 122	-1004708891538
SPT(16)	1038734707889935759	0 108 120 132 150 160 174 190 222 238 252 262 280 292 304 412	-550847083648
SPT(20)	1038735362360605531	0 30 46 160 226 250 256 322 336 348 370 382 396 462 468 492 558 672 688 718	103623586124
STPT(10)	1038735376375510139	0 2 18 20 30 32 42 44 60 62	117638490732
SPT(16)	1038735750052113637	0 60 84 90 156 172 214 280 396 462 504 520 586 592 616 676	491315094230
SPT(16)	1038735917935526353	0 4 36 54 70 78 124 166 168 210 256 264 280 298 330 334	659198506946
TPT(14)	1038735997586088479	0 2 42 44 72 74 168 170 198 200 240 242 270 272	738849069072