Prime p₀= 2568777591590701781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 28 2 22 2 184 2 22 2 (?)
a_n: 0 2 6 8 36 38 66 68 90 92 276 278 300 302
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: 302
Found by: JayPi
db: batch=82, k=14, 4 28 28 22 184 22

SPT(16)	2568775604307476801	0 6 30 80 110 128 156 168 380 392 420 438 468 518 542 548	-1987283224980
STPT(10)	2568776145422049371	0 2 6 8 48 50 90 92 96 98	-1446168652410
SPT(16)	2568776950051688473	0 4 18 30 40 54 58 84 100 126 130 144 154 166 180 184	-641539013308
TPT(14)	2568777097901585717	0 2 24 26 42 44 54 56 84 86 144 146 150 152	-493689116064
STPT(10)	2568777391437258611	0 2 30 32 78 80 126 128 156 158	-200153443170
STPT(10)	2568777543618385859	0 2 42 44 90 92 138 140 180 182	-47972315922
TPT(14)	2568777614472557909	0 2 78 80 120 122 192 194 252 254 330 332 390 392	22881856128
SPT(16)	2568777695629346627	0 30 66 84 110 114 116 122 144 150 152 156 182 200 236 266	104038644846
SPT(16)	2568777752685752869	0 4 10 22 60 100 120 174 508 562 582 622 660 672 678 682	161095051088
SPT(16)	2568777870597896411	0 18 32 80 86 216 236 240 308 312 332 462 468 516 530 548	279007194630
SPT(16)	2568778057823453059	0 90 112 114 124 174 202 234 250 282 310 360 370 372 394 484	466232751278