Prime p₀= 10577911955974499 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 4 2 58 2 10 2 10 2 (?)
a_n: 0 2 12 14 42 44 48 50 108 110 120 122 132 134
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: 134
Found by: crashtech
db: batch=62, k=14, 10 28 4 58 10 10

SPT(14)	10577863530036059	0 8 14 20 38 80 104 138 162 204 222 228 234 242	-48425938440
SPT(14)	10577879266729009	0 42 58 78 112 114 160 162 208 210 244 264 280 322	-32689245490
TPT(12)	10577880820107437	0 2 12 14 72 74 114 116 174 176 180 182	-31135867062
TPT(12)	10577892025407557	0 2 12 14 54 56 90 92 114 116 132 134	-19930566942
TPT(12)	10577892543071729	0 2 12 14 72 74 108 110 150 152 168 170	-19412902770
SPT(14)	10577893475952421	0 10 22 40 42 82 138 190 246 286 288 306 318 328	-18480022078
SPT(14)	10577923170543017	0 14 24 44 50 66 80 90 104 120 126 146 156 170	11214568518
SPT(14)	10577929466119507	0 6 10 34 72 90 114 172 196 214 252 276 280 286	17510145008
SPT(14)	10577931619945471	0 48 60 70 78 88 108 130 150 160 168 178 190 238	19663970972
SPT(14)	10577937600834389	0 8 30 32 38 42 44 78 80 84 90 92 114 122	25644859890
SPT(14)	10577938477056547	0 4 10 34 46 94 106 114 126 174 186 210 216 220	26521082048