Prime p₀= 1635272816538316997 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 28 2 136 2 16 2 22 2 16 2 (?)
a_n: 0 2 84 86 114 116 252 254 270 272 294 296 312 314
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: 314
Found by: rlacr
db: batch=78, k=14, 82 28 136 16 22 16

TPT(14)	1635271747781425931	0 2 36 38 60 62 78 80 126 128 210 212 300 302	-1068756891066
SPT(16)	1635271820418915997	0 30 64 66 70 90 112 132 184 204 226 246 250 252 286 316	-996119401000
STPT(10)	1635271903014720779	0 2 48 50 90 92 132 134 180 182	-913523596218
SPT(16)	1635272068088787103	0 40 54 94 106 114 120 156 244 280 286 294 306 346 360 400	-748449529894
STPT(10)	1635272255163889997	0 2 54 56 72 74 90 92 144 146	-561374427000
STPT(10)	1635272813149783097	0 2 42 44 132 134 222 224 264 266	-3388533900
SPT(16)	1635272876655296951	0 20 36 102 120 128 156 186 242 272 300 308 326 392 408 428	60116979954
SPT(16)	1635272958802953439	0 30 40 90 102 118 132 168 172 208 222 238 250 300 310 340	142264636442
SPT(20)	1635273148960904251	0 28 82 108 142 156 162 178 192 208 210 226 240 256 262 276 310 336 390 418	332422587254
STPT(10)	1635273432291775481	0 2 6 8 18 20 30 32 36 38	615753458484
SPT(16)	1635273832742165267	0 12 14 32 42 44 54 86 150 182 192 194 204 222 224 236	1016203848270