Prime p₀= 2531956184174249741 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 76 2 70 2 28 2 34 2 (?)
a_n: 0 2 30 32 60 62 138 140 210 212 240 242 276 278
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: 278
Found by: JayPi
db: batch=82, k=14, 28 28 76 70 28 34

SPT(16)	2531954769656646163	0 30 36 58 100 118 120 130 186 196 198 216 258 280 286 316	-1414517603578
STPT(10)	2531954910171102461	0 2 48 50 108 110 168 170 216 218	-1274003147280
SPT(16)	2531955084517598513	0 14 78 96 114 116 134 144 170 180 198 200 218 236 300 314	-1099656651228
SPT(16)	2531955101174074241	0 2 80 108 176 180 222 242 246 266 308 312 380 408 486 488	-1083000175500
SPT(16)	2531955759826822877	0 42 44 84 104 116 146 174 182 210 240 252 272 312 314 356	-424347426864
TPT(14)	2531955814507867547	0 2 60 62 114 116 132 134 204 206 330 332 384 386	-369666382194
SPT(16)	2531956232841601957	0 10 54 72 84 174 186 202 234 250 262 352 364 382 426 436	48667352216
SPT(16)	2531956240131558551	0 6 48 62 110 122 168 188 240 260 306 318 366 380 422 428	55957308810
STPT(10)	2531957185474059521	0 2 6 8 48 50 90 92 96 98	1001299809780
SPT(16)	2531957370893435713	0 16 46 78 88 100 114 120 154 160 174 186 196 228 258 274	1186719185972
SPT(16)	2531957645312301187	0 10 22 46 60 72 90 172 174 256 274 286 300 324 336 346	1461138051446