Prime p₀= 1456654620743023811 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 10 2 94 2 28 2 22 2 76 2 (?)
a_n: 0 2 18 20 30 32 126 128 156 158 180 182 258 260
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: 260
Found by: [SG-2W]Kurzer
db: batch=78, k=14, 16 10 94 28 22 76

STPT(10)	1456653527728153421	0 2 6 8 18 20 30 32 36 38	-1093014870390
STPT(10)	1456654017404270537	0 2 30 32 72 74 114 116 144 146	-603338753274
SPT(16)	1456654055347821469	0 24 28 40 118 138 150 220 258 328 340 360 438 450 454 478	-565395202342
SPT(16)	1456654142886445571	0 6 12 68 92 96 126 168 200 242 272 276 300 356 362 368	-477856578240
SPT(16)	1456654261712051761	0 10 22 46 52 196 216 232 240 256 276 420 426 450 462 472	-359030972050
SPT(18)	1456654612749077809	0 34 40 42 48 58 114 124 184 228 288 298 354 364 370 372 378 412	-7993946002
SPT(16)	1456654747754479699	0 4 12 54 108 112 144 174 178 208 240 244 298 340 348 352	127011455888
SPT(16)	1456655173240662481	0 48 72 100 118 130 132 160 438 466 468 480 498 526 550 598	552497638670
SPT(16)	1456655313608859761	0 8 42 50 62 108 122 138 272 288 302 348 360 368 402 410	692865835950
STPT(10)	1456655326549453799	0 2 18 20 30 32 42 44 60 62	705806429988
STPT(10)	1456655532732723077	0 2 30 32 42 44 54 56 84 86	911989699266