Prime p₀= 2591768098627418897 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 82 2 4 2 40 2 40 2 (?)
a_n: 0 2 60 62 90 92 174 176 180 182 222 224 264 266
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: JayPi
db: batch=82, k=14, 58 28 82 4 40 40

TPT(14)	2591766377379622607	0 2 90 92 162 164 192 194 222 224 234 236 420 422	-1721247796290
TPT(14)	2591766442532152889	0 2 12 14 48 50 78 80 108 110 132 134 150 152	-1656095266008
STPT(10)	2591766529619428919	0 2 18 20 30 32 42 44 60 62	-1569007989978
SPT(16)	2591766882701424347	0 6 12 20 44 54 80 86 90 96 122 132 156 164 170 176	-1215925994550
STPT(10)	2591767149125509517	0 2 30 32 42 44 54 56 84 86	-949501909380
STPT(10)	2591767507611141017	0 2 30 32 72 74 114 116 144 146	-591016277880
SPT(16)	2591768218761716429	0 2 14 32 68 74 84 92 120 128 138 144 180 198 210 212	120134297532
SPT(16)	2591768288595748307	0 14 24 56 66 84 96 114 122 140 152 170 180 212 222 236	189968329410
STPT(10)	2591768682271068371	0 2 36 38 78 80 120 122 156 158	583643649474
SPT(13)	2591769060423562157	0 42 84 120 264 270 312 354 360 504 540 582 624	961796143260
SPT(16)	2591769204769007267	0 2 14 30 42 50 56 60 86 90 96 104 116 132 144 146	1106141588370