Prime p₀= 1568525481254308217 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 4 2 28 2 22 2 124 2 22 2 (?)
a_n: 0 2 54 56 60 62 90 92 114 116 240 242 264 266
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: 266
Found by: xii5ku
db: batch=78, k=14, 52 4 28 22 124 22

TPT(14)	1568524522625871779	0 2 48 50 78 80 90 92 150 152 168 170 210 212	-958628436438
SPT(20)	1568524621283451103	0 4 90 108 130 136 166 186 198 250 354 406 418 438 468 474 496 514 600 604	-859970857114
SPT(16)	1568524764551679163	0 4 40 64 84 94 106 130 144 168 180 190 210 234 270 274	-716702629054
STPT(12)	1568525150160697061	0 2 48 50 90 92 126 128 168 170 216 218	-331093611156
STPT(10)	1568525229547906451	0 2 6 8 48 50 90 92 96 98	-251706401766
SPT(16)	1568525279850079567	0 16 90 130 136 174 184 190 240 246 256 294 300 340 414 430	-201404228650
SPT(16)	1568525571196444321	0 52 60 66 108 138 160 216 262 318 340 370 412 418 426 478	89942136104
STPT(10)	1568525845739591897	0 2 30 32 72 74 114 116 144 146	364485283680
STPT(10)	1568526152143328309	0 2 42 44 120 122 198 200 240 242	670889020092
STPT(10)	1568526180442461419	0 2 48 50 90 92 132 134 180 182	699188153202
TPT(14)	1568526568752211301	0 2 30 32 36 38 126 128 186 188 228 230 288 290	1087497903084