Prime p₀= 1264438253452343537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 64 2 10 2 40 2 28 2 4 2 (?)
a_n: 0 2 84 86 150 152 162 164 204 206 234 236 240 242
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: 242
Found by: Megacruncher
db: batch=77, k=14, 82 64 10 40 28 4

STPT(10)	1264436841970589657	0 2 30 32 42 44 54 56 84 86	-1411481753880
STPT(10)	1264437192766546031	0 2 36 38 78 80 120 122 156 158	-1060685797506
SPT(16)	1264437677079169739	0 12 14 90 104 132 188 200 222 234 290 318 332 408 410 422	-576373173798
SPT(16)	1264437702547566667	0 30 42 54 96 156 172 186 250 264 280 340 382 394 406 436	-550904776870
SPT(16)	1264437868074309559	0 12 52 54 60 82 168 190 252 274 360 382 388 390 430 442	-385378033978
SPT(16)	1264437937160304871	0 28 30 138 180 196 210 222 226 238 252 268 310 418 420 448	-316292038666
TPT(14)	1264438329360473609	0 2 12 14 18 20 102 104 222 224 240 242 348 350	75908130072
STPT(10)	1264438470124108397	0 2 30 32 42 44 54 56 84 86	216671764860
SPT(16)	1264439072524710337	0 24 34 100 124 136 150 154 162 166 180 192 216 282 292 316	819072366800
STPT(10)	1264439116866770309	0 2 48 50 90 92 132 134 180 182	863414426772
STPT(10)	1264439192962745867	0 2 12 14 42 44 72 74 84 86	939510402330