Prime p₀= 2568777614472557909 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 70 2 58 2 76 2 58 2 (?)
a_n: 0 2 78 80 120 122 192 194 252 254 330 332 390 392
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: 392
Found by: JayPi
db: batch=82, k=14, 76 40 70 58 76 58

STPT(10)	2568776145422049371	0 2 6 8 48 50 90 92 96 98	-1469050508538
SPT(16)	2568776950051688473	0 4 18 30 40 54 58 84 100 126 130 144 154 166 180 184	-664420869436
TPT(14)	2568777097901585717	0 2 24 26 42 44 54 56 84 86 144 146 150 152	-516570972192
STPT(10)	2568777391437258611	0 2 30 32 78 80 126 128 156 158	-223035299298
STPT(10)	2568777543618385859	0 2 42 44 90 92 138 140 180 182	-70854172050
TPT(14)	2568777591590701781	0 2 6 8 36 38 66 68 90 92 276 278 300 302	-22881856128
SPT(16)	2568777695629346627	0 30 66 84 110 114 116 122 144 150 152 156 182 200 236 266	81156788718
SPT(16)	2568777752685752869	0 4 10 22 60 100 120 174 508 562 582 622 660 672 678 682	138213194960
SPT(16)	2568777870597896411	0 18 32 80 86 216 236 240 308 312 332 462 468 516 530 548	256125338502
SPT(16)	2568778057823453059	0 90 112 114 124 174 202 234 250 282 310 360 370 372 394 484	443350895150
SPT(16)	2568778182437278853	0 6 56 66 86 90 104 114 116 126 140 144 164 174 224 230	567964720944