Prime p₀= 4400374383782504339 starts a Symmetric tuple of 14 consecutive primes, which form 7 twin primes (STPT).
d_n: 0 2 16 2 22 2 16 2 16 2 22 2 16 2 (?)
a_n: 0 2 18 20 42 44 60 62 78 80 102 104 120 122
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: 122
Found by: [SG]KidDoesCrunch
db: batch=85, k=14, 2 16 2 22 2 16 2

SPT(16)	4400372786721954491	0 8 18 42 50 102 126 138 140 152 176 228 236 260 270 278	-1597060549848
SPT(16)	4400372948141190169	0 84 100 114 118 132 142 162 190 210 220 234 238 252 268 352	-1435641314170
SPT(16)	4400373016473160819	0 78 82 88 112 144 192 264 388 460 508 540 564 570 574 652	-1367309343520
SPT(16)	4400374214525845739	0 2 14 42 68 72 74 84 128 138 140 144 170 198 210 212	-169256658600
STPT(10)	4400374333886824127	0 2 42 44 102 104 162 164 204 206	-49895680212
STPT(10)	4400374335647786339	0 2 18 20 30 32 42 44 60 62	-48134718000
TPT(14)	4400374383782504339	0 2 18 20 42 44 60 62 78 80 102 104 120 122	0
STPT(10)	4400374684717539557	0 2 30 32 42 44 54 56 84 86	300935035218
TPT(14)	4400375154956710931	0 2 66 68 138 140 150 152 180 182 240 242 306 308	771174206592
SPT(16)	4400375169008722837	0 72 82 90 96 120 124 154 162 192 196 220 226 234 244 316	785226218498
SPT(16)	4400375586703830367	0 22 34 54 60 90 96 142 144 190 196 226 232 252 264 286	1202921326028