Prime p₀= 2044729766887788677 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 28 2 10 2 178 2 124 2 (?)
a_n: 0 2 12 14 72 74 102 104 114 116 294 296 420 422
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: 422
Found by: Dingo
db: batch=80, k=14, 10 58 28 10 178 124

SPT(16)	2044728627472466269	0 10 64 94 102 132 138 154 228 244 250 280 288 318 372 382	-1139415322408
STPT(12)	2044728698510027069	0 2 12 14 72 74 78 80 138 140 150 152	-1068377761608
SPT(16)	2044728964986777149	0 54 68 72 80 98 108 110 192 194 204 222 230 234 248 302	-801901011528
SPT(16)	2044729200628007617	0 22 70 72 114 142 174 196 240 262 294 322 364 366 414 436	-566259781060
STPT(10)	2044729665954365441	0 2 6 8 18 20 30 32 36 38	-100933423236
STPT(10)	2044729707759681947	0 2 42 44 132 134 222 224 264 266	-59128106730
SPT(16)	2044729894502874739	0 52 54 58 88 130 154 168 184 198 222 264 294 298 300 352	127615086062
TPT(14)	2044729901812654319	0 2 168 170 180 182 228 230 240 242 258 260 282 284	134924865642
SPT(16)	2044729965618193199	0 20 48 68 78 108 110 114 188 192 194 224 234 254 282 302	198730404522
STPT(10)	2044730353021352987	0 2 12 14 42 44 72 74 84 86	586133564310
STPT(10)	2044730470731760697	0 2 30 32 72 74 114 116 144 146	703843972020