Prime p₀= 1144124768210971751 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 58 2 106 2 28 2 28 2 (?)
a_n: 0 2 66 68 78 80 138 140 246 248 276 278 306 308
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: 308
Found by: Theadalus
db: batch=76, k=14, 64 10 58 106 28 28

SPT(16)	1144123941438384469	0 30 84 118 132 142 150 154 198 202 210 220 234 268 322 352	-826772587282
SPT(16)	1144123944741314857	0 12 22 36 40 52 60 82 150 172 180 192 196 210 220 232	-823469656894
SPT(16)	1144124162742289433	0 8 48 74 78 80 110 134 150 174 204 206 210 236 276 284	-605468682318
SPT(18)	1144124520132183097	0 30 34 70 84 96 100 120 132 154 166 186 190 202 216 252 256 286	-248078788654
STPT(10)	1144124545634655251	0 2 6 8 18 20 30 32 36 38	-222576316500
STPT(10)	1144124653207732319	0 2 12 14 30 32 48 50 60 62	-115003239432
SPT(16)	1144124852301888623	0 36 56 78 90 126 158 168 236 246 278 314 326 348 368 404	84090916872
SPT(13)	1144125270043942477	0 12 30 90 102 126 156 186 210 222 282 300 312	501832970726
STPT(10)	1144125323560679729	0 2 78 80 150 152 222 224 300 302	555349707978
STPT(12)	1144125474515989487	0 2 12 14 54 56 90 92 132 134 144 146	706305017736
SPT(16)	1144125578820712591	0 12 42 78 82 148 162 166 252 256 270 336 340 376 406 418	810609740840