Prime p₀= 2569853931287469731 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 40 2 94 2 22 2 76 2 (?)
a_n: 0 2 36 38 48 50 90 92 186 188 210 212 288 290
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: 290
Found by: JayPi
db: batch=82, k=14, 34 10 40 94 22 76

TPT(14)	2569850971389382727	0 2 12 14 54 56 60 62 72 74 90 92 102 104	-2959898087004
STPT(10)	2569851178947199331	0 2 30 32 60 62 90 92 120 122	-2752340270400
STPT(10)	2569851982393962779	0 2 42 44 60 62 78 80 120 122	-1948893506952
STPT(10)	2569852906497497891	0 2 6 8 48 50 90 92 96 98	-1024789971840
STPT(10)	2569853099416446659	0 2 12 14 30 32 48 50 60 62	-831871023072
SPT(16)	2569853222955670049	0 48 80 132 180 194 224 234 308 318 348 362 410 462 494 542	-708331799682
TPT(14)	2569854212024281067	0 2 30 32 72 74 84 86 114 116 144 146 240 242	280736811336
SPT(16)	2569854251201421227	0 24 26 86 116 156 186 194 492 500 530 570 600 660 662 686	319913951496
TPT(14)	2569854377285968679	0 2 12 14 18 20 30 32 60 62 210 212 240 242	445998498948
STPT(10)	2569854643431575699	0 2 12 14 90 92 168 170 180 182	712144105968
SPT(16)	2569854891362859203	0 6 24 26 78 80 104 146 168 210 234 236 288 290 308 314	960075389472