Prime p₀= 2727519574674196901 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 70 2 10 2 16 2 10 2 64 2 (?)
a_n: 0 2 126 128 198 200 210 212 228 230 240 242 306 308
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: 308
Found by: JayPi
db: batch=82, k=14, 124 70 10 16 10 64

SPT(16)	2727517732622332483	0 28 40 60 144 148 168 184 234 250 270 274 358 378 390 418	-1842051864418
STPT(10)	2727518127945497099	0 2 12 14 90 92 168 170 180 182	-1446728699802
TPT(14)	2727518867328717701	0 2 30 32 96 98 108 110 120 122 126 128 156 158	-707345479200
SPT(16)	2727518900537542297	0 42 60 70 96 114 130 132 154 156 172 190 216 226 244 286	-674136654604
SPT(16)	2727519138635593123	0 30 64 84 100 106 126 136 174 184 204 210 226 246 280 310	-436038603778
SPT(16)	2727519434649677897	0 6 14 92 120 186 206 342 344 480 500 566 594 672 680 686	-140024519004
SPT(16)	2727519646007106737	0 36 42 50 86 90 92 122 174 204 206 210 246 254 260 296	71332909836
SPT(16)	2727520121200866829	0 18 60 78 90 138 168 178 204 214 244 292 304 322 364 382	546526669928
SPT(16)	2727520307675604899	0 14 30 42 104 128 134 150 152 168 174 198 260 272 288 302	733001407998
SPT(16)	2727520310047131971	0 60 72 78 120 140 162 170 198 206 228 248 290 296 308 368	735372935070
STPT(10)	2727520417569490967	0 2 54 56 72 74 90 92 144 146	842895294066