Prime p₀= 2119947017117097527 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 22 2 16 2 58 2 106 2 (?)
a_n: 0 2 30 32 60 62 84 86 102 104 162 164 270 272
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: 272
Found by: Landjunge
db: batch=80, k=14, 28 28 22 16 58 106

TPT(14)	2119946322322383809	0 2 60 62 78 80 102 104 210 212 282 284 312 314	-694794713718
STPT(10)	2119946414891755361	0 2 6 8 18 20 30 32 36 38	-602225342166
SPT(16)	2119946533128273163	0 6 28 30 40 94 138 166 168 196 240 294 304 306 328 334	-483988824364
SPT(16)	2119946759447099743	0 18 88 90 174 208 244 250 264 270 306 340 424 426 496 514	-257669997784
STPT(10)	2119946894621363909	0 2 12 14 90 92 168 170 180 182	-122495733618
TPT(14)	2119946903791214747	0 2 12 14 30 32 42 44 54 56 60 62 72 74	-113325882780
SPT(16)	2119947063141699613	0 34 66 78 90 118 126 136 138 148 156 184 196 208 240 274	46024602086
STPT(10)	2119947097494312209	0 2 12 14 30 32 48 50 60 62	80377214682
STPT(10)	2119947575976248069	0 2 42 44 60 62 78 80 120 122	558859150542
SPT(16)	2119948798062182603	0 8 20 36 66 90 120 138 176 194 224 248 278 294 306 314	1780945085076
SPT(16)	2119949300579323487	0 66 80 96 102 126 140 180 182 222 236 260 266 282 296 362	2283462225960