Prime p₀= 3016087824976027271 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 52 2 28 2 4 2 82 2 (?)
a_n: 0 2 30 32 66 68 120 122 150 152 156 158 240 242
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: ginga
db: batch=82, k=14, 28 34 52 28 4 82

TPT(14)	3016086565954984799	0 2 30 32 60 62 90 92 102 104 132 134 198 200	-1259021042472
TPT(14)	3016087054282126211	0 2 30 32 36 38 78 80 90 92 126 128 228 230	-770693901060
TPT(14)	3016087142845947197	0 2 42 44 84 86 144 146 150 152 252 254 264 266	-682130080074
STPT(10)	3016087521316957457	0 2 30 32 42 44 54 56 84 86	-303659069814
SPT(16)	3016087684806370507	0 4 12 42 82 124 126 222 244 340 342 384 424 454 462 466	-140169656764
STPT(10)	3016087747199459729	0 2 18 20 30 32 42 44 60 62	-77776567542
SPT(16)	3016088010242641679	0 14 20 38 42 44 72 92 120 140 168 170 174 192 198 212	185266614408
SPT(16)	3016088496058436299	0 4 18 22 30 34 70 90 112 132 168 172 180 184 198 202	671082409028
STPT(10)	3016088803134658871	0 2 6 8 48 50 90 92 96 98	978158631600
STPT(10)	3016088998676282531	0 2 30 32 60 62 90 92 120 122	1173700255260
SPT(16)	3016089039066428669	0 14 32 42 60 78 92 114 308 330 344 362 380 390 408 422	1214090401398