Prime p₀= 2501675316530363159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 28 2 4 2 100 2 28 2 (?)
a_n: 0 2 30 32 102 104 132 134 138 140 240 242 270 272
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: 272
Found by: [SG-FC] hl
db: batch=82, k=14, 28 70 28 4 100 28

SPT(18)	2501673387277353937	0 22 76 84 112 124 154 156 162 244 250 252 282 294 322 330 384 406	-1929253009222
SPT(16)	2501673416473580119	0 24 60 64 72 94 102 130 162 190 198 220 228 232 268 292	-1900056783040
SPT(16)	2501673591944132843	0 18 30 90 156 188 194 228 266 300 306 338 404 464 476 494	-1724586230316
STPT(10)	2501673707628061157	0 2 42 44 72 74 102 104 144 146	-1608902302002
STPT(10)	2501673969624220607	0 2 60 62 72 74 84 86 144 146	-1346906142552
SPT(16)	2501674168456980203	0 30 56 60 98 114 120 134 150 164 170 186 224 228 254 284	-1148073382956
SPT(20)	2501675493504512459	0 12 38 68 80 140 164 168 170 180 212 222 224 228 252 312 324 354 380 392	176974149300
STPT(10)	2501675600024543441	0 2 36 38 78 80 120 122 156 158	283494180282
TPT(14)	2501675604275842781	0 2 78 80 90 92 138 140 150 152 180 182 276 278	287745479622
SPT(16)	2501676031264935541	0 42 52 132 136 142 150 162 190 202 210 216 220 300 310 352	714734572382
SPT(16)	2501676728295711983	0 8 38 90 120 150 168 198 260 290 308 338 368 420 450 458	1411765348824