Prime p₀= 4044828756832784717 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 238 2 10 2 220 2 4 2 40 2 40 2 (?)
a_n: 0 2 240 242 252 254 474 476 480 482 522 524 564 566
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: 566
Found by: Alnitak2019
db: batch=84, k=14, 238 10 220 4 40 40

SPT(16)	4044827602977226003	0 58 70 94 124 168 178 184 330 336 346 390 420 444 456 514	-1153855558714
SPT(16)	4044827939591882341	0 22 28 30 42 90 106 132 136 162 178 226 238 240 246 268	-817240902376
SPT(16)	4044828126921112673	0 6 18 86 90 116 140 156 158 174 198 224 228 296 308 314	-629911672044
STPT(10)	4044828163529172989	0 2 12 14 30 32 48 50 60 62	-593303611728
SPT(16)	4044828333604944091	0 16 40 82 108 118 120 150 208 238 240 250 276 318 342 358	-423227840626
SPT(16)	4044828344177067649	0 12 82 88 90 112 138 222 250 334 360 382 384 390 460 472	-412655717068
STPT(10)	4044828780312926729	0 2 12 14 30 32 48 50 60 62	23480142012
TPT(14)	4044828849140192159	0 2 12 14 48 50 60 62 132 134 138 140 168 170	92307407442
STPT(12)	4044829111017687359	0 2 12 14 42 44 78 80 108 110 120 122	354184902642
STPT(10)	4044829155941387237	0 2 54 56 72 74 90 92 144 146	399108602520
STPT(10)	4044829685182875599	0 2 48 50 90 92 132 134 180 182	928350090882