Prime p₀= 1297972544840742467 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 40 2 46 2 10 2 28 2 34 2 (?)
a_n: 0 2 12 14 54 56 102 104 114 116 144 146 180 182
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: 182
Found by: Cruncher Pete
db: batch=77, k=14, 10 40 46 10 28 34

SPT(16)	1297971415760272807	0 10 16 46 94 112 114 126 130 142 144 162 210 240 246 256	-1129080469660
TPT(14)	1297971422344610147	0 2 12 14 24 26 54 56 114 116 180 182 450 452	-1122496132320
SPT(16)	1297971425112444839	0 12 38 54 80 108 138 168 194 224 254 282 308 324 350 362	-1119728297628
SPT(16)	1297971463122936761	0 8 56 78 96 102 110 126 302 318 326 332 350 372 420 428	-1081717805706
SPT(16)	1297972080426338521	0 42 70 112 136 150 190 210 232 252 292 306 330 372 400 442	-464414403946
SPT(16)	1297972373413391213	0 14 38 44 54 80 108 128 150 170 198 224 234 240 264 278	-171427351254
SPT(16)	1297972945713197011	0 18 40 60 70 88 96 112 126 142 150 168 178 198 220 238	400872454544
SPT(16)	1297973098135040099	0 12 38 62 68 80 110 134 168 192 222 234 240 264 290 302	553294297632
SPT(16)	1297973245733917759	0 4 10 30 42 48 90 132 220 262 304 310 322 342 348 352	700893175292
STPT(12)	1297973314769203571	0 2 48 50 78 80 90 92 120 122 168 170	769928461104
STPT(10)	1297973584084159061	0 2 30 32 78 80 126 128 156 158	1039243416594