Prime p₀= 2290563454025204999 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 70 2 76 2 28 2 100 2 (?)
a_n: 0 2 42 44 60 62 132 134 210 212 240 242 342 344
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: 344
Found by: Landjunge
db: batch=81, k=14, 40 16 70 76 28 100

SPT(16)	2290562186869574897	0 6 12 56 86 116 140 144 152 156 180 210 240 284 290 296	-1267155630102
STPT(10)	2290562354681880437	0 2 54 56 72 74 90 92 144 146	-1099343324562
SPT(16)	2290562503672009453	0 6 54 108 138 154 174 256 258 340 360 376 406 460 508 514	-950353195546
STPT(10)	2290562889281775137	0 2 30 32 42 44 54 56 84 86	-564743429862
SPT(16)	2290563248883478073	0 26 30 86 116 156 170 228 278 336 350 390 420 476 480 506	-205141726926
TPT(14)	2290563380210204399	0 2 108 110 198 200 210 212 222 224 240 242 312 314	-73815000600
SPT(16)	2290563657009597569	0 8 20 62 98 152 194 200 372 378 420 474 510 552 564 572	202984392570
SPT(16)	2290563676700403443	0 6 8 26 44 80 120 164 180 224 264 300 318 336 338 344	222675198444
STPT(10)	2290564241284235009	0 2 30 32 60 62 90 92 120 122	787259030010
SPT(16)	2290564617390361591	0 48 58 76 88 90 102 138 160 196 208 210 222 240 250 298	1163365156592
STPT(10)	2290564798583084921	0 2 30 32 120 122 210 212 240 242	1344557879922