Prime p₀= 1133977505409242237 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 46 2 22 2 64 2 28 2 10 2 (?)
a_n: 0 2 72 74 120 122 144 146 210 212 240 242 252 254
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: 254
Found by: stoneageman
db: batch=76, k=14, 70 46 22 64 28 10

SPT(16)	1133976064352223923	0 36 56 134 158 176 188 216 278 306 318 336 360 438 458 494	-1441057018314
STPT(10)	1133976115999067387	0 2 54 56 72 74 90 92 144 146	-1389410174850
STPT(10)	1133976497007504089	0 2 30 32 60 62 90 92 120 122	-1008401738148
SPT(16)	1133976635309632307	0 6 36 50 110 116 140 162 194 216 240 246 306 320 350 356	-870099609930
SPT(16)	1133977025972802241	0 40 48 60 66 70 76 132 136 192 198 202 208 220 228 268	-479436439996
STPT(10)	1133977470045329051	0 2 6 8 18 20 30 32 36 38	-35363913186
SPT(16)	1133977702034066177	0 30 60 80 92 116 126 156 170 200 210 234 246 266 296 326	196624823940
STPT(10)	1133978100497667179	0 2 18 20 30 32 42 44 60 62	595088424942
STPT(10)	1133978266147694789	0 2 48 50 90 92 132 134 180 182	760738452552
STPT(10)	1133978396630775539	0 2 18 20 30 32 42 44 60 62	891221533302
SPT(16)	1133978730017816899	0 30 60 72 84 90 102 112 132 142 154 160 172 184 214 244	1224608574662