Prime p₀= 1728720596971507127 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 130 2 34 2 58 2 112 2 (?)
a_n: 0 2 30 32 72 74 204 206 240 242 300 302 414 416
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: 416
Found by: CoolAtchOk
db: batch=79, k=14, 28 40 130 34 58 112

SPT(16)	1728718729929247619	0 8 12 14 30 38 68 104 198 234 264 272 288 290 294 302	-1867042259508
STPT(10)	1728719376326372357	0 2 30 32 72 74 114 116 144 146	-1220645134770
SPT(16)	1728719707988198473	0 28 30 66 78 84 88 144 160 216 220 226 238 274 276 304	-888983308654
SPT(16)	1728719894328249149	0 38 42 60 78 98 110 140 162 192 204 224 242 260 264 302	-702643257978
TPT(14)	1728719924231546537	0 2 102 104 144 146 210 212 282 284 390 392 420 422	-672739960590
STPT(10)	1728720567332263787	0 2 42 44 72 74 102 104 144 146	-29639243340
STPT(12)	1728720672464043521	0 2 30 32 90 92 168 170 228 230 258 260	75492536394
SPT(18)	1728721177708162189	0 10 34 48 54 84 142 160 168 184 192 210 268 298 304 318 342 352	580736655062
SPT(16)	1728721206109642981	0 12 40 52 70 132 162 196 216 250 280 342 360 372 400 412	609138135854
STPT(10)	1728721381314165419	0 2 18 20 30 32 42 44 60 62	784342658292
SPT(16)	1728721475451698009	0 14 18 24 72 128 162 164 168 170 204 260 308 314 318 332	878480190882