Prime p₀= 2200951850128688729 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 22 2 16 2 28 2 76 2 70 2 (?)
a_n: 0 2 48 50 72 74 90 92 120 122 198 200 270 272
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: 272
Found by: Penguin
db: batch=81, k=14, 46 22 16 28 76 70

STPT(10)	2200950526150650917	0 2 24 26 42 44 60 62 84 86	-1323978037812
TPT(14)	2200951080147843227	0 2 72 74 120 122 150 152 162 164 180 182 240 242	-769980845502
STPT(10)	2200951354937926139	0 2 48 50 90 92 132 134 180 182	-495190762590
STPT(10)	2200951535535875999	0 2 30 32 60 62 90 92 120 122	-314592812730
SPT(16)	2200951572844447063	0 18 54 78 84 90 106 120 124 138 154 160 166 190 226 244	-277284241666
SPT(16)	2200951782892425839	0 14 20 30 68 78 108 132 170 194 224 234 272 282 288 302	-67236262890
SPT(16)	2200951956986197937	0 30 54 56 60 74 110 140 156 186 222 236 240 242 266 296	106857509208
SPT(16)	2200952248321622563	0 4 6 36 88 136 160 174 190 204 228 276 328 358 360 364	398192933834
SPT(16)	2200952696891701219	0 18 42 52 60 90 108 132 148 172 190 220 228 238 262 280	846763012490
STPT(10)	2200953085344582431	0 2 36 38 78 80 120 122 156 158	1235215893702
SPT(16)	2200953204089251673	0 18 68 74 80 90 98 158 216 276 284 294 300 306 356 374	1353960562944