Prime p₀= 2499285944641237721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 76 2 40 2 28 2 88 2 (?)
a_n: 0 2 30 32 60 62 138 140 180 182 210 212 300 302
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: Penguin
db: batch=82, k=14, 28 28 76 40 28 88

TPT(14)	2499283453037907617	0 2 30 32 42 44 54 56 102 104 180 182 222 224	-2491603330104
STPT(10)	2499283506127370087	0 2 30 32 72 74 114 116 144 146	-2438513867634
SPT(16)	2499283522565963657	0 12 20 42 44 72 80 122 132 174 182 210 212 234 242 254	-2422075274064
STPT(10)	2499284384166238619	0 2 18 20 30 32 42 44 60 62	-1560474999102
STPT(10)	2499285148454787389	0 2 12 14 90 92 168 170 180 182	-796186450332
STPT(10)	2499285381055649369	0 2 78 80 120 122 162 164 240 242	-563585588352
SPT(16)	2499286106818994081	0 8 30 78 86 110 116 138 158 180 186 210 218 266 288 296	162177756360
STPT(10)	2499286146763353929	0 2 42 44 60 62 78 80 120 122	202122116208
STPT(12)	2499286528342493117	0 2 42 44 54 56 60 62 72 74 114 116	583701255396
STPT(10)	2499286802704441961	0 2 30 32 78 80 126 128 156 158	858063204240
SPT(16)	2499286860205866869	0 14 24 48 78 90 102 110 132 140 152 164 194 218 228 242	915564629148