Prime p₀= 3016087142845947197 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 58 2 4 2 100 2 10 2 (?)
a_n: 0 2 42 44 84 86 144 146 150 152 252 254 264 266
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: 266
Found by: ginga
db: batch=82, k=14, 40 40 58 4 100 10

SPT(16)	3016085756046643493	0 6 50 56 98 126 146 176 180 210 230 258 300 306 350 356	-1386799303704
SPT(16)	3016085836960353607	0 36 46 64 72 76 106 130 216 240 270 274 282 300 310 346	-1305885593590
SPT(16)	3016085839753071713	0 18 78 116 134 138 144 168 176 200 206 210 228 266 326 344	-1303092875484
TPT(14)	3016086421035746867	0 2 30 32 54 56 90 92 132 134 144 146 174 176	-721810200330
TPT(14)	3016086565954984799	0 2 30 32 60 62 90 92 102 104 132 134 198 200	-576890962398
TPT(14)	3016087054282126211	0 2 30 32 36 38 78 80 90 92 126 128 228 230	-88563820986
STPT(10)	3016087521316957457	0 2 30 32 42 44 54 56 84 86	378471010260
SPT(16)	3016087684806370507	0 4 12 42 82 124 126 222 244 340 342 384 424 454 462 466	541960423310
STPT(10)	3016087747199459729	0 2 18 20 30 32 42 44 60 62	604353512532
TPT(14)	3016087824976027271	0 2 30 32 66 68 120 122 150 152 156 158 240 242	682130080074
SPT(16)	3016088010242641679	0 14 20 38 42 44 72 92 120 140 168 170 174 192 198 212	867396694482